id	sid	tid	token	lemma	pos
ap-7354	1	1	acta	acta	PROPN
ap-7354	1	2	polytechnica	polytechnica	PROPN
ap-7354	1	3	https://doi.org/10.14311/ap.2021.61.0689	https://doi.org/10.14311/ap.2021.61.0689	PROPN
ap-7354	1	4	acta	acta	PROPN
ap-7354	1	5	polytechnica	polytechnica	PROPN
ap-7354	1	6	61(6):689–702	61(6):689–702	PROPN
ap-7354	1	7	,	,	PUNCT
ap-7354	1	8	2021	2021	NUM
ap-7354	1	9	©	©	ADP
ap-7354	1	10	2021	2021	NUM
ap-7354	1	11	the	the	DET
ap-7354	1	12	author(s	author(s	NOUN
ap-7354	1	13	)	)	PUNCT
ap-7354	1	14	.	.	PUNCT
ap-7354	2	1	licensed	license	VERB
ap-7354	2	2	under	under	ADP
ap-7354	2	3	a	a	DET
ap-7354	2	4	cc	cc	NOUN
ap-7354	2	5	-	-	PUNCT
ap-7354	2	6	by	by	ADP
ap-7354	2	7	4.0	4.0	NUM
ap-7354	2	8	licence	licence	NOUN
ap-7354	2	9	published	publish	VERB
ap-7354	2	10	by	by	ADP
ap-7354	2	11	the	the	DET
ap-7354	2	12	czech	czech	PROPN
ap-7354	2	13	technical	technical	PROPN
ap-7354	2	14	university	university	PROPN
ap-7354	2	15	in	in	ADP
ap-7354	2	16	prague	prague	PROPN
ap-7354	2	17	dirac	dirac	PROPN
ap-7354	2	18	oscillator	oscillator	NOUN
ap-7354	2	19	in	in	ADP
ap-7354	2	20	dynamical	dynamical	ADJ
ap-7354	2	21	noncommutative	noncommutative	ADJ
ap-7354	2	22	space	space	NOUN
ap-7354	2	23	ilyas	ilyas	PROPN
ap-7354	2	24	haouam	haouam	PROPN
ap-7354	2	25	université	université	PROPN
ap-7354	2	26	frères	frère	NOUN
ap-7354	2	27	mentouri	mentouri	PROPN
ap-7354	2	28	,	,	PUNCT
ap-7354	2	29	laboratoire	laboratoire	PROPN
ap-7354	2	30	de	de	X
ap-7354	2	31	physique	physique	PROPN
ap-7354	2	32	mathématique	mathématique	X
ap-7354	2	33	et	et	X
ap-7354	2	34	de	de	X
ap-7354	2	35	physique	physique	PROPN
ap-7354	2	36	subatomique	subatomique	NOUN
ap-7354	2	37	(	(	PUNCT
ap-7354	2	38	lpmps	lpmp	NOUN
ap-7354	2	39	)	)	PUNCT
ap-7354	2	40	,	,	PUNCT
ap-7354	2	41	constantine	constantine	PROPN
ap-7354	2	42	25000	25000	NUM
ap-7354	2	43	,	,	PUNCT
ap-7354	2	44	algeria	algeria	PROPN
ap-7354	2	45	correspondence	correspondence	NOUN
ap-7354	2	46	:	:	PUNCT
ap-7354	2	47	ilyashaouam@live.fr	ilyashaouam@live.fr	PROPN
ap-7354	2	48	abstract	abstract	NOUN
ap-7354	2	49	.	.	PUNCT
ap-7354	3	1	in	in	ADP
ap-7354	3	2	this	this	DET
ap-7354	3	3	paper	paper	NOUN
ap-7354	3	4	,	,	PUNCT
ap-7354	3	5	we	we	PRON
ap-7354	3	6	address	address	VERB
ap-7354	3	7	the	the	DET
ap-7354	3	8	energy	energy	NOUN
ap-7354	3	9	eigenvalues	eigenvalue	NOUN
ap-7354	3	10	of	of	ADP
ap-7354	3	11	two	two	NUM
ap-7354	3	12	-	-	PUNCT
ap-7354	3	13	dimensional	dimensional	ADJ
ap-7354	3	14	dirac	dirac	NOUN
ap-7354	3	15	oscillator	oscillator	NOUN
ap-7354	3	16	perturbed	perturb	VERB
ap-7354	3	17	by	by	ADP
ap-7354	3	18	a	a	DET
ap-7354	3	19	dynamical	dynamical	ADJ
ap-7354	3	20	noncommutative	noncommutative	ADJ
ap-7354	3	21	space	space	NOUN
ap-7354	3	22	.	.	PUNCT
ap-7354	4	1	we	we	PRON
ap-7354	4	2	derived	derive	VERB
ap-7354	4	3	the	the	DET
ap-7354	4	4	relativistic	relativistic	ADJ
ap-7354	4	5	hamiltonian	hamiltonian	NOUN
ap-7354	4	6	of	of	ADP
ap-7354	4	7	dirac	dirac	NOUN
ap-7354	4	8	oscillator	oscillator	NOUN
ap-7354	4	9	in	in	ADP
ap-7354	4	10	the	the	DET
ap-7354	4	11	dynamical	dynamical	ADJ
ap-7354	4	12	noncommutative	noncommutative	ADJ
ap-7354	4	13	space	space	NOUN
ap-7354	4	14	,	,	PUNCT
ap-7354	4	15	in	in	ADP
ap-7354	4	16	which	which	PRON
ap-7354	4	17	the	the	DET
ap-7354	4	18	space	space	NOUN
ap-7354	4	19	-	-	PUNCT
ap-7354	4	20	space	space	NOUN
ap-7354	4	21	heisenberg	heisenberg	PROPN
ap-7354	4	22	-	-	PUNCT
ap-7354	4	23	like	like	ADJ
ap-7354	4	24	commutation	commutation	NOUN
ap-7354	4	25	relations	relation	NOUN
ap-7354	4	26	and	and	CCONJ
ap-7354	4	27	noncommutative	noncommutative	ADJ
ap-7354	4	28	parameter	parameter	NOUN
ap-7354	4	29	are	be	AUX
ap-7354	4	30	position	position	NOUN
ap-7354	4	31	-	-	PUNCT
ap-7354	4	32	dependent	dependent	ADJ
ap-7354	4	33	.	.	PUNCT
ap-7354	5	1	then	then	ADV
ap-7354	5	2	,	,	PUNCT
ap-7354	5	3	we	we	PRON
ap-7354	5	4	used	use	VERB
ap-7354	5	5	this	this	DET
ap-7354	5	6	hamiltonian	hamiltonian	NOUN
ap-7354	5	7	to	to	PART
ap-7354	5	8	calculate	calculate	VERB
ap-7354	5	9	the	the	DET
ap-7354	5	10	first	first	ADJ
ap-7354	5	11	-	-	PUNCT
ap-7354	5	12	order	order	NOUN
ap-7354	5	13	correction	correction	NOUN
ap-7354	5	14	to	to	ADP
ap-7354	5	15	the	the	DET
ap-7354	5	16	eigenvalues	eigenvalue	NOUN
ap-7354	5	17	and	and	CCONJ
ap-7354	5	18	eigenvectors	eigenvector	NOUN
ap-7354	5	19	,	,	PUNCT
ap-7354	5	20	based	base	VERB
ap-7354	5	21	on	on	ADP
ap-7354	5	22	the	the	DET
ap-7354	5	23	language	language	NOUN
ap-7354	5	24	of	of	ADP
ap-7354	5	25	creation	creation	NOUN
ap-7354	5	26	and	and	CCONJ
ap-7354	5	27	annihilation	annihilation	NOUN
ap-7354	5	28	operators	operator	NOUN
ap-7354	5	29	and	and	CCONJ
ap-7354	5	30	using	use	VERB
ap-7354	5	31	the	the	DET
ap-7354	5	32	perturbation	perturbation	NOUN
ap-7354	5	33	theory	theory	NOUN
ap-7354	5	34	.	.	PUNCT
ap-7354	6	1	it	it	PRON
ap-7354	6	2	is	be	AUX
ap-7354	6	3	shown	show	VERB
ap-7354	6	4	that	that	SCONJ
ap-7354	6	5	the	the	DET
ap-7354	6	6	energy	energy	NOUN
ap-7354	6	7	shift	shift	NOUN
ap-7354	6	8	depends	depend	VERB
ap-7354	6	9	on	on	ADP
ap-7354	6	10	the	the	DET
ap-7354	6	11	dynamical	dynamical	ADJ
ap-7354	6	12	noncommutative	noncommutative	ADJ
ap-7354	6	13	parameter	parameter	PROPN
ap-7354	6	14	τ	τ	PROPN
ap-7354	6	15	.	.	PUNCT
ap-7354	7	1	knowing	know	VERB
ap-7354	7	2	that	that	SCONJ
ap-7354	7	3	,	,	PUNCT
ap-7354	7	4	with	with	ADP
ap-7354	7	5	a	a	DET
ap-7354	7	6	set	set	NOUN
ap-7354	7	7	of	of	ADP
ap-7354	7	8	two	two	NUM
ap-7354	7	9	-	-	PUNCT
ap-7354	7	10	dimensional	dimensional	ADJ
ap-7354	7	11	bopp	bopp	VERB
ap-7354	7	12	-	-	PUNCT
ap-7354	7	13	shift	shift	NOUN
ap-7354	7	14	transformation	transformation	NOUN
ap-7354	7	15	,	,	PUNCT
ap-7354	7	16	we	we	PRON
ap-7354	7	17	mapped	map	VERB
ap-7354	7	18	the	the	DET
ap-7354	7	19	noncommutative	noncommutative	ADJ
ap-7354	7	20	problem	problem	NOUN
ap-7354	7	21	to	to	ADP
ap-7354	7	22	the	the	DET
ap-7354	7	23	standard	standard	ADJ
ap-7354	7	24	commutative	commutative	ADJ
ap-7354	7	25	one	one	NUM
ap-7354	7	26	.	.	PUNCT
ap-7354	8	1	keywords	keyword	NOUN
ap-7354	8	2	:	:	PUNCT
ap-7354	8	3	dynamical	dynamical	ADJ
ap-7354	8	4	noncommutative	noncommutative	ADJ
ap-7354	8	5	space	space	NOUN
ap-7354	8	6	,	,	PUNCT
ap-7354	8	7	τ	τ	PROPN
ap-7354	8	8	-space	-space	NOUN
ap-7354	8	9	,	,	PUNCT
ap-7354	8	10	noncommutative	noncommutative	ADJ
ap-7354	8	11	dirac	dirac	PROPN
ap-7354	8	12	oscillator	oscillator	NOUN
ap-7354	8	13	,	,	PUNCT
ap-7354	8	14	perturbation	perturbation	NOUN
ap-7354	8	15	theory	theory	NOUN
ap-7354	8	16	.	.	PUNCT
ap-7354	9	1	1	1	X
ap-7354	9	2	.	.	X
ap-7354	9	3	introduction	introduction	NOUN
ap-7354	9	4	in	in	ADP
ap-7354	9	5	the	the	DET
ap-7354	9	6	last	last	ADJ
ap-7354	9	7	few	few	ADJ
ap-7354	9	8	decades	decade	NOUN
ap-7354	9	9	,	,	PUNCT
ap-7354	9	10	physicists	physicist	NOUN
ap-7354	9	11	and	and	CCONJ
ap-7354	9	12	mathematicians	mathematician	NOUN
ap-7354	9	13	have	have	AUX
ap-7354	9	14	developed	develop	VERB
ap-7354	9	15	a	a	DET
ap-7354	9	16	mathematical	mathematical	ADJ
ap-7354	9	17	theory	theory	NOUN
ap-7354	9	18	called	call	VERB
ap-7354	9	19	noncommutative	noncommutative	PROPN
ap-7354	9	20	geometry	geometry	NOUN
ap-7354	9	21	,	,	PUNCT
ap-7354	9	22	which	which	PRON
ap-7354	9	23	has	have	AUX
ap-7354	9	24	quickly	quickly	ADV
ap-7354	9	25	become	become	VERB
ap-7354	9	26	a	a	DET
ap-7354	9	27	topic	topic	NOUN
ap-7354	9	28	of	of	ADP
ap-7354	9	29	great	great	ADJ
ap-7354	9	30	interest	interest	NOUN
ap-7354	9	31	and	and	CCONJ
ap-7354	9	32	has	have	AUX
ap-7354	9	33	been	be	AUX
ap-7354	9	34	finding	find	VERB
ap-7354	9	35	applications	application	NOUN
ap-7354	9	36	in	in	ADP
ap-7354	9	37	many	many	ADJ
ap-7354	9	38	areas	area	NOUN
ap-7354	9	39	of	of	ADP
ap-7354	9	40	modern	modern	ADJ
ap-7354	9	41	physics	physic	NOUN
ap-7354	9	42	,	,	PUNCT
ap-7354	9	43	such	such	ADJ
ap-7354	9	44	as	as	ADP
ap-7354	9	45	high	high	ADJ
ap-7354	9	46	energy	energy	NOUN
ap-7354	9	47	[	[	X
ap-7354	9	48	1	1	NUM
ap-7354	9	49	]	]	PUNCT
ap-7354	9	50	,	,	PUNCT
ap-7354	9	51	cosmology	cosmology	NOUN
ap-7354	10	1	[	[	X
ap-7354	10	2	2	2	NUM
ap-7354	10	3	,	,	PUNCT
ap-7354	10	4	3	3	NUM
ap-7354	10	5	]	]	PUNCT
ap-7354	10	6	,	,	PUNCT
ap-7354	10	7	gravity	gravity	NOUN
ap-7354	10	8	[	[	X
ap-7354	10	9	4	4	NUM
ap-7354	10	10	]	]	PUNCT
ap-7354	10	11	,	,	PUNCT
ap-7354	10	12	quantum	quantum	ADJ
ap-7354	10	13	physics	physics	NOUN
ap-7354	11	1	[	[	X
ap-7354	11	2	5–7	5–7	X
ap-7354	11	3	]	]	PUNCT
ap-7354	11	4	and	and	CCONJ
ap-7354	11	5	field	field	NOUN
ap-7354	11	6	theory	theory	NOUN
ap-7354	11	7	[	[	X
ap-7354	11	8	8	8	NUM
ap-7354	11	9	,	,	PUNCT
ap-7354	11	10	9	9	NUM
ap-7354	11	11	]	]	PUNCT
ap-7354	11	12	.	.	PUNCT
ap-7354	12	1	substantially	substantially	ADV
ap-7354	12	2	,	,	PUNCT
ap-7354	12	3	the	the	DET
ap-7354	12	4	study	study	NOUN
ap-7354	12	5	on	on	ADP
ap-7354	12	6	noncommutative	noncommutative	ADJ
ap-7354	12	7	(	(	PUNCT
ap-7354	12	8	nc	nc	NOUN
ap-7354	12	9	)	)	PUNCT
ap-7354	12	10	spaces	space	NOUN
ap-7354	12	11	is	be	AUX
ap-7354	12	12	very	very	ADV
ap-7354	12	13	important	important	ADJ
ap-7354	12	14	for	for	ADP
ap-7354	12	15	understanding	understand	VERB
ap-7354	12	16	phenomena	phenomenon	NOUN
ap-7354	12	17	at	at	ADP
ap-7354	12	18	a	a	DET
ap-7354	12	19	tiny	tiny	ADJ
ap-7354	12	20	scale	scale	NOUN
ap-7354	12	21	of	of	ADP
ap-7354	12	22	physical	physical	ADJ
ap-7354	12	23	theories	theory	NOUN
ap-7354	12	24	.	.	PUNCT
ap-7354	13	1	the	the	DET
ap-7354	13	2	idea	idea	NOUN
ap-7354	13	3	behind	behind	ADP
ap-7354	13	4	the	the	DET
ap-7354	13	5	extension	extension	NOUN
ap-7354	13	6	of	of	ADP
ap-7354	13	7	noncommutativity	noncommutativity	NOUN
ap-7354	13	8	to	to	ADP
ap-7354	13	9	the	the	DET
ap-7354	13	10	coordinates	coordinate	NOUN
ap-7354	13	11	was	be	AUX
ap-7354	13	12	first	first	ADV
ap-7354	13	13	suggested	suggest	VERB
ap-7354	13	14	by	by	ADP
ap-7354	13	15	heisenberg	heisenberg	PROPN
ap-7354	13	16	in	in	ADP
ap-7354	13	17	1930	1930	NUM
ap-7354	13	18	as	as	ADP
ap-7354	13	19	a	a	DET
ap-7354	13	20	solution	solution	NOUN
ap-7354	13	21	to	to	PART
ap-7354	13	22	remove	remove	VERB
ap-7354	13	23	the	the	DET
ap-7354	13	24	infinite	infinite	ADJ
ap-7354	13	25	quantities	quantity	NOUN
ap-7354	13	26	of	of	ADP
ap-7354	13	27	field	field	NOUN
ap-7354	13	28	theories	theory	NOUN
ap-7354	13	29	.	.	PUNCT
ap-7354	14	1	the	the	DET
ap-7354	14	2	nc	nc	PROPN
ap-7354	14	3	space	space	NOUN
ap-7354	14	4	-	-	PUNCT
ap-7354	14	5	time	time	NOUN
ap-7354	14	6	structures	structure	NOUN
ap-7354	14	7	were	be	AUX
ap-7354	14	8	first	first	ADV
ap-7354	14	9	mentioned	mention	VERB
ap-7354	14	10	by	by	ADP
ap-7354	14	11	snyder	snyder	PROPN
ap-7354	14	12	in	in	ADP
ap-7354	14	13	1947	1947	NUM
ap-7354	14	14	[	[	X
ap-7354	14	15	10	10	NUM
ap-7354	14	16	,	,	PUNCT
ap-7354	14	17	11	11	NUM
ap-7354	14	18	]	]	PUNCT
ap-7354	14	19	,	,	PUNCT
ap-7354	14	20	in	in	ADP
ap-7354	14	21	which	which	PRON
ap-7354	14	22	he	he	PRON
ap-7354	14	23	introduced	introduce	VERB
ap-7354	14	24	noncommutativity	noncommutativity	NOUN
ap-7354	14	25	in	in	ADP
ap-7354	14	26	the	the	DET
ap-7354	14	27	hope	hope	NOUN
ap-7354	14	28	of	of	ADP
ap-7354	14	29	regularizing	regularize	VERB
ap-7354	14	30	the	the	DET
ap-7354	14	31	divergencies	divergency	NOUN
ap-7354	14	32	that	that	PRON
ap-7354	14	33	plagued	plague	VERB
ap-7354	14	34	quantum	quantum	ADJ
ap-7354	14	35	field	field	NOUN
ap-7354	14	36	theory	theory	NOUN
ap-7354	14	37	.	.	PUNCT
ap-7354	15	1	motivated	motivate	VERB
ap-7354	15	2	by	by	ADP
ap-7354	15	3	the	the	DET
ap-7354	15	4	attempts	attempt	NOUN
ap-7354	15	5	to	to	PART
ap-7354	15	6	understand	understand	VERB
ap-7354	15	7	the	the	DET
ap-7354	15	8	string	string	NOUN
ap-7354	15	9	theory	theory	NOUN
ap-7354	15	10	,	,	PUNCT
ap-7354	15	11	the	the	DET
ap-7354	15	12	quantum	quantum	ADJ
ap-7354	15	13	gravitation	gravitation	NOUN
ap-7354	15	14	and	and	CCONJ
ap-7354	15	15	black	black	ADJ
ap-7354	15	16	holes	hole	NOUN
ap-7354	15	17	through	through	ADP
ap-7354	15	18	nc	nc	PROPN
ap-7354	15	19	spaces	space	NOUN
ap-7354	15	20	and	and	CCONJ
ap-7354	15	21	by	by	ADP
ap-7354	15	22	seeking	seek	VERB
ap-7354	15	23	to	to	PART
ap-7354	15	24	highlight	highlight	VERB
ap-7354	15	25	more	more	ADJ
ap-7354	15	26	phenomenological	phenomenological	ADJ
ap-7354	15	27	implications	implication	NOUN
ap-7354	15	28	,	,	PUNCT
ap-7354	15	29	we	we	PRON
ap-7354	15	30	consider	consider	VERB
ap-7354	15	31	the	the	DET
ap-7354	15	32	dirac	dirac	NOUN
ap-7354	15	33	oscillator	oscillator	NOUN
ap-7354	15	34	(	(	PUNCT
ap-7354	15	35	do	do	AUX
ap-7354	15	36	)	)	PUNCT
ap-7354	15	37	within	within	ADP
ap-7354	15	38	a	a	DET
ap-7354	15	39	two	two	NUM
ap-7354	15	40	-	-	PUNCT
ap-7354	15	41	dimensional	dimensional	ADJ
ap-7354	15	42	dynamical	dynamical	ADJ
ap-7354	15	43	noncommutative	noncommutative	NOUN
ap-7354	15	44	(	(	PUNCT
ap-7354	15	45	dnc	dnc	PROPN
ap-7354	15	46	)	)	PUNCT
ap-7354	15	47	space	space	NOUN
ap-7354	15	48	(	(	PUNCT
ap-7354	15	49	also	also	ADV
ap-7354	15	50	known	know	VERB
ap-7354	15	51	as	as	ADP
ap-7354	15	52	a	a	DET
ap-7354	15	53	position	position	NOUN
ap-7354	15	54	-	-	PUNCT
ap-7354	15	55	dependent	dependent	ADJ
ap-7354	15	56	nc	nc	PROPN
ap-7354	15	57	space	space	NOUN
ap-7354	15	58	)	)	PUNCT
ap-7354	15	59	.	.	PUNCT
ap-7354	16	1	unlike	unlike	ADP
ap-7354	16	2	the	the	DET
ap-7354	16	3	simplest	simple	ADJ
ap-7354	16	4	possible	possible	ADJ
ap-7354	16	5	type	type	NOUN
ap-7354	16	6	of	of	ADP
ap-7354	16	7	nc	nc	PROPN
ap-7354	16	8	spaces	space	NOUN
ap-7354	16	9	,	,	PUNCT
ap-7354	16	10	in	in	ADP
ap-7354	16	11	which	which	PRON
ap-7354	16	12	the	the	DET
ap-7354	16	13	nc	nc	PROPN
ap-7354	16	14	parameter	parameter	PROPN
ap-7354	16	15	is	be	AUX
ap-7354	16	16	constant	constant	ADJ
ap-7354	16	17	,	,	PUNCT
ap-7354	16	18	here	here	ADV
ap-7354	16	19	we	we	PRON
ap-7354	16	20	talk	talk	VERB
ap-7354	16	21	about	about	ADP
ap-7354	16	22	a	a	DET
ap-7354	16	23	different	different	ADJ
ap-7354	16	24	type	type	NOUN
ap-7354	16	25	of	of	ADP
ap-7354	16	26	nc	nc	PROPN
ap-7354	16	27	spaces	space	NOUN
ap-7354	16	28	,	,	PUNCT
ap-7354	16	29	where	where	SCONJ
ap-7354	16	30	the	the	DET
ap-7354	16	31	deformation	deformation	NOUN
ap-7354	16	32	parameter	parameter	NOUN
ap-7354	16	33	will	will	AUX
ap-7354	16	34	no	no	ADV
ap-7354	16	35	longer	long	ADV
ap-7354	16	36	be	be	AUX
ap-7354	16	37	constant	constant	ADJ
ap-7354	16	38	.	.	PUNCT
ap-7354	17	1	however	however	ADV
ap-7354	17	2	,	,	PUNCT
ap-7354	17	3	there	there	PRON
ap-7354	17	4	are	be	VERB
ap-7354	17	5	many	many	ADJ
ap-7354	17	6	other	other	ADJ
ap-7354	17	7	possibilities	possibility	NOUN
ap-7354	17	8	that	that	PRON
ap-7354	17	9	can	can	AUX
ap-7354	17	10	not	not	PART
ap-7354	17	11	be	be	AUX
ap-7354	17	12	excluded	exclude	VERB
ap-7354	17	13	.	.	PUNCT
ap-7354	18	1	in	in	ADP
ap-7354	18	2	fact	fact	NOUN
ap-7354	18	3	,	,	PUNCT
ap-7354	18	4	in	in	ADP
ap-7354	18	5	the	the	DET
ap-7354	18	6	first	first	ADJ
ap-7354	18	7	paper	paper	NOUN
ap-7354	18	8	by	by	ADP
ap-7354	18	9	snyder	snyder	PROPN
ap-7354	18	10	himself	himself	PRON
ap-7354	18	11	[	[	X
ap-7354	18	12	10	10	NUM
ap-7354	18	13	]	]	PUNCT
ap-7354	18	14	,	,	PUNCT
ap-7354	18	15	the	the	DET
ap-7354	18	16	noncommutativity	noncommutativity	NOUN
ap-7354	18	17	parameter	parameter	NOUN
ap-7354	18	18	was	be	AUX
ap-7354	18	19	taken	take	VERB
ap-7354	18	20	to	to	PART
ap-7354	18	21	depend	depend	VERB
ap-7354	18	22	on	on	ADP
ap-7354	18	23	the	the	DET
ap-7354	18	24	coordinates	coordinate	NOUN
ap-7354	18	25	and	and	CCONJ
ap-7354	18	26	the	the	DET
ap-7354	18	27	momenta	momenta	PROPN
ap-7354	18	28	.	.	PUNCT
ap-7354	19	1	considerable	considerable	ADJ
ap-7354	19	2	different	different	ADJ
ap-7354	19	3	possibilities	possibility	NOUN
ap-7354	19	4	have	have	AUX
ap-7354	19	5	been	be	AUX
ap-7354	19	6	explored	explore	VERB
ap-7354	19	7	since	since	SCONJ
ap-7354	19	8	then	then	ADV
ap-7354	19	9	,	,	PUNCT
ap-7354	19	10	especially	especially	ADV
ap-7354	19	11	in	in	ADP
ap-7354	19	12	the	the	DET
ap-7354	19	13	lie	lie	NOUN
ap-7354	19	14	-	-	PUNCT
ap-7354	19	15	algebraic	algebraic	ADJ
ap-7354	19	16	approaches	approach	VERB
ap-7354	19	17	[	[	X
ap-7354	19	18	12	12	NUM
ap-7354	19	19	]	]	PUNCT
ap-7354	19	20	,	,	PUNCT
ap-7354	19	21	κ	κ	NOUN
ap-7354	19	22	-	-	PUNCT
ap-7354	19	23	poincaré	poincaré	ADJ
ap-7354	19	24	noncommutativity	noncommutativity	NOUN
ap-7354	19	25	[	[	X
ap-7354	19	26	13	13	NUM
ap-7354	19	27	]	]	PUNCT
ap-7354	19	28	,	,	PUNCT
ap-7354	19	29	other	other	ADJ
ap-7354	19	30	fuzzy	fuzzy	ADJ
ap-7354	19	31	spaces	space	NOUN
ap-7354	19	32	[	[	X
ap-7354	19	33	14	14	NUM
ap-7354	19	34	]	]	PUNCT
ap-7354	19	35	.	.	PUNCT
ap-7354	20	1	besides	besides	SCONJ
ap-7354	20	2	,	,	PUNCT
ap-7354	20	3	more	more	ADV
ap-7354	20	4	recently	recently	ADV
ap-7354	20	5	in	in	ADP
ap-7354	20	6	position	position	NOUN
ap-7354	20	7	-	-	PUNCT
ap-7354	20	8	dependent	dependent	ADJ
ap-7354	20	9	approach	approach	NOUN
ap-7354	20	10	[	[	X
ap-7354	20	11	15–17	15–17	NUM
ap-7354	20	12	]	]	PUNCT
ap-7354	20	13	,	,	PUNCT
ap-7354	20	14	the	the	DET
ap-7354	20	15	authors	author	NOUN
ap-7354	20	16	considered	consider	VERB
ap-7354	20	17	θµν	θµν	PRON
ap-7354	20	18	to	to	PART
ap-7354	20	19	be	be	AUX
ap-7354	20	20	a	a	DET
ap-7354	20	21	function	function	NOUN
ap-7354	20	22	of	of	ADP
ap-7354	20	23	the	the	DET
ap-7354	20	24	position	position	NOUN
ap-7354	20	25	coordinates	coordinate	NOUN
ap-7354	20	26	,	,	PUNCT
ap-7354	20	27	i.e.	i.e.	X
ap-7354	20	28	,	,	PUNCT
ap-7354	20	29	θ→θ(x	θ→θ(x	ADJ
ap-7354	20	30	,	,	PUNCT
ap-7354	20	31	y	y	PROPN
ap-7354	20	32	)	)	PUNCT
ap-7354	20	33	.	.	PUNCT
ap-7354	21	1	the	the	DET
ap-7354	21	2	relativistic	relativistic	ADJ
ap-7354	21	3	do	do	AUX
ap-7354	21	4	has	have	VERB
ap-7354	21	5	a	a	DET
ap-7354	21	6	great	great	ADJ
ap-7354	21	7	potential	potential	NOUN
ap-7354	21	8	both	both	CCONJ
ap-7354	21	9	for	for	ADP
ap-7354	21	10	the	the	DET
ap-7354	21	11	theoretical	theoretical	ADJ
ap-7354	21	12	and	and	CCONJ
ap-7354	21	13	practical	practical	ADJ
ap-7354	21	14	applications	application	NOUN
ap-7354	21	15	.	.	PUNCT
ap-7354	22	1	the	the	DET
ap-7354	22	2	potential	potential	ADJ
ap-7354	22	3	term	term	NOUN
ap-7354	22	4	is	be	AUX
ap-7354	22	5	introduced	introduce	VERB
ap-7354	22	6	linearly	linearly	ADV
ap-7354	22	7	,	,	PUNCT
ap-7354	22	8	by	by	ADP
ap-7354	22	9	substitution	substitution	NOUN
ap-7354	22	10	−→p	−→p	NOUN
ap-7354	22	11	→	→	SYM
ap-7354	22	12	−→p	−→p	NOUN
ap-7354	22	13	−	−	NOUN
ap-7354	22	14	imβω−→r	imβω−→r	NOUN
ap-7354	22	15	in	in	ADP
ap-7354	22	16	free	free	ADJ
ap-7354	22	17	dirac	dirac	NOUN
ap-7354	22	18	hamiltonian	hamiltonian	NOUN
ap-7354	22	19	,	,	PUNCT
ap-7354	22	20	this	this	PRON
ap-7354	22	21	was	be	AUX
ap-7354	22	22	considered	consider	VERB
ap-7354	22	23	for	for	ADP
ap-7354	22	24	the	the	DET
ap-7354	22	25	first	first	ADJ
ap-7354	22	26	time	time	NOUN
ap-7354	22	27	by	by	ADP
ap-7354	22	28	ito	ito	PROPN
ap-7354	22	29	et	et	PROPN
ap-7354	22	30	al	al	PROPN
ap-7354	22	31	.	.	PUNCT
ap-7354	23	1	[	[	X
ap-7354	23	2	18	18	NUM
ap-7354	23	3	]	]	PUNCT
ap-7354	23	4	,	,	PUNCT
ap-7354	23	5	with	with	ADP
ap-7354	23	6	−→r	−→r	PRON
ap-7354	23	7	being	be	AUX
ap-7354	23	8	the	the	DET
ap-7354	23	9	position	position	NOUN
ap-7354	23	10	vector	vector	NOUN
ap-7354	23	11	and	and	CCONJ
ap-7354	23	12	m	m	PROPN
ap-7354	23	13	,	,	PUNCT
ap-7354	23	14	β	β	X
ap-7354	23	15	,	,	PUNCT
ap-7354	23	16	ω	ω	X
ap-7354	23	17	>	>	X
ap-7354	23	18	0	0	PUNCT
ap-7354	23	19	being	be	AUX
ap-7354	23	20	the	the	DET
ap-7354	23	21	rest	rest	NOUN
ap-7354	23	22	mass	mass	NOUN
ap-7354	23	23	of	of	ADP
ap-7354	23	24	the	the	DET
ap-7354	23	25	particle	particle	NOUN
ap-7354	23	26	,	,	PUNCT
ap-7354	23	27	dirac	dirac	NOUN
ap-7354	23	28	matrix	matrix	NOUN
ap-7354	23	29	and	and	CCONJ
ap-7354	23	30	constant	constant	ADJ
ap-7354	23	31	oscillator	oscillator	NOUN
ap-7354	23	32	frequency	frequency	NOUN
ap-7354	23	33	,	,	PUNCT
ap-7354	23	34	respectively	respectively	ADV
ap-7354	23	35	.	.	PUNCT
ap-7354	24	1	it	it	PRON
ap-7354	24	2	was	be	AUX
ap-7354	24	3	named	name	VERB
ap-7354	24	4	dirac	dirac	NOUN
ap-7354	24	5	oscillator	oscillator	NOUN
ap-7354	24	6	by	by	ADP
ap-7354	24	7	moshinsky	moshinsky	PROPN
ap-7354	24	8	and	and	CCONJ
ap-7354	24	9	szczepaniak	szczepaniak	NOUN
ap-7354	24	10	[	[	X
ap-7354	24	11	19	19	NUM
ap-7354	24	12	]	]	PUNCT
ap-7354	24	13	because	because	SCONJ
ap-7354	24	14	it	it	PRON
ap-7354	24	15	is	be	AUX
ap-7354	24	16	a	a	DET
ap-7354	24	17	relativistic	relativistic	ADJ
ap-7354	24	18	generalization	generalization	NOUN
ap-7354	24	19	of	of	ADP
ap-7354	24	20	the	the	DET
ap-7354	24	21	non	non	ADJ
ap-7354	24	22	-	-	ADJ
ap-7354	24	23	relativistic	relativistic	ADJ
ap-7354	24	24	harmonic	harmonic	ADJ
ap-7354	24	25	oscillator	oscillator	NOUN
ap-7354	24	26	and	and	CCONJ
ap-7354	24	27	,	,	PUNCT
ap-7354	24	28	exactly	exactly	ADV
ap-7354	24	29	in	in	ADP
ap-7354	24	30	a	a	DET
ap-7354	24	31	non	non	ADJ
ap-7354	24	32	-	-	ADJ
ap-7354	24	33	relativistic	relativistic	ADJ
ap-7354	24	34	limit	limit	NOUN
ap-7354	24	35	,	,	PUNCT
ap-7354	24	36	it	it	PRON
ap-7354	24	37	reduces	reduce	VERB
ap-7354	24	38	to	to	ADP
ap-7354	24	39	a	a	DET
ap-7354	24	40	standard	standard	ADJ
ap-7354	24	41	harmonic	harmonic	ADJ
ap-7354	24	42	oscillator	oscillator	NOUN
ap-7354	24	43	with	with	ADP
ap-7354	24	44	a	a	DET
ap-7354	24	45	strong	strong	ADJ
ap-7354	24	46	spin	spin	NOUN
ap-7354	24	47	-	-	PUNCT
ap-7354	24	48	orbit	orbit	NOUN
ap-7354	24	49	coupling	coupling	NOUN
ap-7354	24	50	term	term	NOUN
ap-7354	24	51	.	.	PUNCT
ap-7354	25	1	physically	physically	ADV
ap-7354	25	2	,	,	PUNCT
ap-7354	25	3	do	do	AUX
ap-7354	25	4	has	have	AUX
ap-7354	25	5	attracted	attract	VERB
ap-7354	25	6	a	a	DET
ap-7354	25	7	lot	lot	NOUN
ap-7354	25	8	of	of	ADP
ap-7354	25	9	attention	attention	NOUN
ap-7354	25	10	because	because	SCONJ
ap-7354	25	11	of	of	ADP
ap-7354	25	12	its	its	PRON
ap-7354	25	13	considerable	considerable	ADJ
ap-7354	25	14	physical	physical	ADJ
ap-7354	25	15	applications	application	NOUN
ap-7354	25	16	,	,	PUNCT
ap-7354	25	17	it	it	PRON
ap-7354	25	18	is	be	AUX
ap-7354	25	19	widely	widely	ADV
ap-7354	25	20	studied	study	VERB
ap-7354	25	21	and	and	CCONJ
ap-7354	25	22	illustrated	illustrate	VERB
ap-7354	25	23	.	.	PUNCT
ap-7354	26	1	it	it	PRON
ap-7354	26	2	can	can	AUX
ap-7354	26	3	be	be	AUX
ap-7354	26	4	shown	show	VERB
ap-7354	26	5	that	that	SCONJ
ap-7354	26	6	it	it	PRON
ap-7354	26	7	is	be	AUX
ap-7354	26	8	a	a	DET
ap-7354	26	9	physical	physical	ADJ
ap-7354	26	10	system	system	NOUN
ap-7354	26	11	,	,	PUNCT
ap-7354	26	12	which	which	PRON
ap-7354	26	13	can	can	AUX
ap-7354	26	14	be	be	AUX
ap-7354	26	15	interpreted	interpret	VERB
ap-7354	26	16	as	as	ADP
ap-7354	26	17	an	an	DET
ap-7354	26	18	interaction	interaction	NOUN
ap-7354	26	19	of	of	ADP
ap-7354	26	20	the	the	DET
ap-7354	26	21	anomalous	anomalous	ADJ
ap-7354	26	22	magnetic	magnetic	ADJ
ap-7354	26	23	moment	moment	NOUN
ap-7354	26	24	with	with	ADP
ap-7354	26	25	a	a	DET
ap-7354	26	26	linear	linear	ADJ
ap-7354	26	27	electric	electric	ADJ
ap-7354	26	28	field	field	NOUN
ap-7354	27	1	[	[	X
ap-7354	27	2	20	20	NUM
ap-7354	27	3	]	]	PUNCT
ap-7354	27	4	.	.	PUNCT
ap-7354	28	1	in	in	ADP
ap-7354	28	2	addition	addition	NOUN
ap-7354	28	3	,	,	PUNCT
ap-7354	28	4	it	it	PRON
ap-7354	28	5	can	can	AUX
ap-7354	28	6	be	be	AUX
ap-7354	28	7	associated	associate	VERB
ap-7354	28	8	with	with	ADP
ap-7354	28	9	the	the	DET
ap-7354	28	10	electromagnetic	electromagnetic	ADJ
ap-7354	28	11	potential	potential	NOUN
ap-7354	28	12	[	[	X
ap-7354	28	13	21	21	NUM
ap-7354	28	14	]	]	PUNCT
ap-7354	28	15	.	.	PUNCT
ap-7354	29	1	as	as	ADP
ap-7354	29	2	an	an	DET
ap-7354	29	3	exactly	exactly	ADV
ap-7354	29	4	solvable	solvable	ADJ
ap-7354	29	5	model	model	NOUN
ap-7354	29	6	,	,	PUNCT
ap-7354	29	7	do	do	AUX
ap-7354	29	8	in	in	ADP
ap-7354	29	9	the	the	DET
ap-7354	29	10	background	background	NOUN
ap-7354	29	11	of	of	ADP
ap-7354	29	12	a	a	DET
ap-7354	29	13	perpendicular	perpendicular	ADJ
ap-7354	29	14	uniform	uniform	ADJ
ap-7354	29	15	magnetic	magnetic	ADJ
ap-7354	29	16	field	field	NOUN
ap-7354	29	17	has	have	AUX
ap-7354	29	18	been	be	AUX
ap-7354	29	19	widely	widely	ADV
ap-7354	29	20	studied	study	VERB
ap-7354	29	21	.	.	PUNCT
ap-7354	30	1	however	however	ADV
ap-7354	30	2	,	,	PUNCT
ap-7354	30	3	we	we	PRON
ap-7354	30	4	mention	mention	VERB
ap-7354	30	5	,	,	PUNCT
ap-7354	30	6	for	for	ADP
ap-7354	30	7	instance	instance	NOUN
ap-7354	30	8	,	,	PUNCT
ap-7354	30	9	the	the	DET
ap-7354	30	10	following	following	NOUN
ap-7354	30	11	:	:	PUNCT
ap-7354	30	12	in	in	ADP
ap-7354	30	13	ref	ref	NOUN
ap-7354	30	14	.	.	PUNCT
ap-7354	31	1	[	[	X
ap-7354	31	2	19	19	NUM
ap-7354	31	3	]	]	PUNCT
ap-7354	31	4	,	,	PUNCT
ap-7354	31	5	the	the	DET
ap-7354	31	6	spectra	spectra	NOUN
ap-7354	31	7	of	of	ADP
ap-7354	31	8	(	(	PUNCT
ap-7354	31	9	3	3	NUM
ap-7354	31	10	+	+	NOUN
ap-7354	31	11	1)-dimensional	1)-dimensional	ADJ
ap-7354	31	12	do	do	AUX
ap-7354	31	13	are	be	AUX
ap-7354	31	14	solved	solve	VERB
ap-7354	31	15	and	and	CCONJ
ap-7354	31	16	the	the	DET
ap-7354	31	17	non	non	ADJ
ap-7354	31	18	-	-	ADJ
ap-7354	31	19	relativistic	relativistic	ADJ
ap-7354	31	20	limit	limit	NOUN
ap-7354	31	21	is	be	AUX
ap-7354	31	22	discussed	discuss	VERB
ap-7354	31	23	,	,	PUNCT
ap-7354	31	24	as	as	ADV
ap-7354	31	25	well	well	ADV
ap-7354	31	26	,	,	PUNCT
ap-7354	31	27	in	in	ADP
ap-7354	31	28	ref	ref	NOUN
ap-7354	31	29	.	.	PUNCT
ap-7354	32	1	[	[	X
ap-7354	32	2	22	22	NUM
ap-7354	32	3	]	]	PUNCT
ap-7354	32	4	,	,	PUNCT
ap-7354	32	5	the	the	DET
ap-7354	32	6	symmetrical	symmetrical	ADJ
ap-7354	32	7	properties	property	NOUN
ap-7354	32	8	of	of	ADP
ap-7354	32	9	the	the	DET
ap-7354	32	10	do	do	NOUN
ap-7354	32	11	are	be	AUX
ap-7354	32	12	studied	study	VERB
ap-7354	32	13	.	.	PUNCT
ap-7354	33	1	the	the	DET
ap-7354	33	2	operators	operator	NOUN
ap-7354	33	3	of	of	ADP
ap-7354	33	4	shift	shift	NOUN
ap-7354	33	5	for	for	ADP
ap-7354	33	6	symmetries	symmetry	NOUN
ap-7354	33	7	are	be	AUX
ap-7354	33	8	constructed	construct	VERB
ap-7354	33	9	explicitly	explicitly	ADV
ap-7354	33	10	[	[	X
ap-7354	33	11	23	23	NUM
ap-7354	33	12	]	]	PUNCT
ap-7354	33	13	.	.	PUNCT
ap-7354	34	1	interestingly	interestingly	ADV
ap-7354	34	2	,	,	PUNCT
ap-7354	34	3	the	the	DET
ap-7354	34	4	do	do	NOUN
ap-7354	34	5	may	may	AUX
ap-7354	34	6	offer	offer	VERB
ap-7354	34	7	a	a	DET
ap-7354	34	8	new	new	ADJ
ap-7354	34	9	approach	approach	NOUN
ap-7354	34	10	to	to	PART
ap-7354	34	11	study	study	VERB
ap-7354	34	12	quantum	quantum	ADJ
ap-7354	34	13	optics	optic	NOUN
ap-7354	34	14	,	,	PUNCT
ap-7354	34	15	where	where	SCONJ
ap-7354	34	16	it	it	PRON
ap-7354	34	17	was	be	AUX
ap-7354	34	18	found	find	VERB
ap-7354	34	19	689	689	NUM
ap-7354	34	20	https://doi.org/10.14311/ap.2021.61.0689	https://doi.org/10.14311/ap.2021.61.0689	ADJ
ap-7354	34	21	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7354	34	22	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7354	34	23	ilyas	ilyas	PROPN
ap-7354	34	24	haouam	haouam	VERB
ap-7354	34	25	acta	acta	PROPN
ap-7354	34	26	polytechnica	polytechnica	PROPN
ap-7354	34	27	that	that	SCONJ
ap-7354	34	28	there	there	PRON
ap-7354	34	29	is	be	VERB
ap-7354	34	30	an	an	DET
ap-7354	34	31	exact	exact	ADJ
ap-7354	34	32	map	map	NOUN
ap-7354	34	33	from	from	ADP
ap-7354	34	34	(	(	PUNCT
ap-7354	34	35	2	2	NUM
ap-7354	34	36	+	+	NOUN
ap-7354	34	37	1)-dimensional	1)-dimensional	ADJ
ap-7354	34	38	do	do	NOUN
ap-7354	34	39	to	to	ADP
ap-7354	34	40	jaynes	jaynes	PROPN
ap-7354	34	41	-	-	PUNCT
ap-7354	34	42	cummings	cummings	PROPN
ap-7354	34	43	(	(	PUNCT
ap-7354	34	44	jc	jc	PROPN
ap-7354	34	45	)	)	PUNCT
ap-7354	34	46	model	model	NOUN
ap-7354	34	47	[	[	X
ap-7354	34	48	24	24	NUM
ap-7354	34	49	]	]	PUNCT
ap-7354	34	50	,	,	PUNCT
ap-7354	34	51	which	which	PRON
ap-7354	34	52	describes	describe	VERB
ap-7354	34	53	the	the	DET
ap-7354	34	54	atomic	atomic	ADJ
ap-7354	34	55	transitions	transition	NOUN
ap-7354	34	56	in	in	ADP
ap-7354	34	57	a	a	DET
ap-7354	34	58	two	two	NUM
ap-7354	34	59	level	level	NOUN
ap-7354	34	60	system	system	NOUN
ap-7354	34	61	.	.	PUNCT
ap-7354	35	1	subsequently	subsequently	ADV
ap-7354	35	2	,	,	PUNCT
ap-7354	35	3	it	it	PRON
ap-7354	35	4	was	be	AUX
ap-7354	35	5	found	find	VERB
ap-7354	35	6	that	that	SCONJ
ap-7354	35	7	this	this	DET
ap-7354	35	8	model	model	NOUN
ap-7354	35	9	can	can	AUX
ap-7354	35	10	be	be	AUX
ap-7354	35	11	mapped	map	VERB
ap-7354	35	12	either	either	ADV
ap-7354	35	13	to	to	ADP
ap-7354	35	14	jc	jc	PROPN
ap-7354	35	15	or	or	CCONJ
ap-7354	35	16	anti	anti	ADJ
ap-7354	35	17	-	-	ADJ
ap-7354	35	18	jc	jc	ADJ
ap-7354	35	19	models	model	NOUN
ap-7354	35	20	,	,	PUNCT
ap-7354	35	21	depending	depend	VERB
ap-7354	35	22	on	on	ADP
ap-7354	35	23	the	the	DET
ap-7354	35	24	magnitude	magnitude	NOUN
ap-7354	35	25	of	of	ADP
ap-7354	35	26	the	the	DET
ap-7354	35	27	magnetic	magnetic	ADJ
ap-7354	35	28	field	field	NOUN
ap-7354	36	1	[	[	X
ap-7354	36	2	25	25	NUM
ap-7354	36	3	]	]	PUNCT
ap-7354	36	4	.	.	PUNCT
ap-7354	37	1	basically	basically	ADV
ap-7354	37	2	,	,	PUNCT
ap-7354	37	3	do	do	AUX
ap-7354	37	4	became	become	VERB
ap-7354	37	5	more	more	ADV
ap-7354	37	6	and	and	CCONJ
ap-7354	37	7	more	more	ADV
ap-7354	37	8	important	important	ADJ
ap-7354	37	9	since	since	SCONJ
ap-7354	37	10	the	the	DET
ap-7354	37	11	experimental	experimental	ADJ
ap-7354	37	12	observations	observation	NOUN
ap-7354	37	13	.	.	PUNCT
ap-7354	38	1	for	for	ADP
ap-7354	38	2	instance	instance	NOUN
ap-7354	38	3	,	,	PUNCT
ap-7354	38	4	we	we	PRON
ap-7354	38	5	mention	mention	VERB
ap-7354	38	6	that	that	SCONJ
ap-7354	38	7	franco	franco	NOUN
ap-7354	38	8	-	-	PUNCT
ap-7354	38	9	villafañe	villafañe	PROPN
ap-7354	38	10	et	et	PROPN
ap-7354	38	11	al	al	PROPN
ap-7354	38	12	.	.	PUNCT
ap-7354	39	1	[	[	X
ap-7354	39	2	26	26	NUM
ap-7354	39	3	]	]	PUNCT
ap-7354	39	4	came	come	VERB
ap-7354	39	5	with	with	ADP
ap-7354	39	6	the	the	DET
ap-7354	39	7	proposal	proposal	NOUN
ap-7354	39	8	of	of	ADP
ap-7354	39	9	a	a	DET
ap-7354	39	10	first	first	ADJ
ap-7354	39	11	-	-	PUNCT
ap-7354	39	12	experimental	experimental	ADJ
ap-7354	39	13	microwave	microwave	NOUN
ap-7354	39	14	realisation	realisation	NOUN
ap-7354	39	15	of	of	ADP
ap-7354	39	16	the	the	DET
ap-7354	39	17	one	one	NUM
ap-7354	39	18	-	-	PUNCT
ap-7354	39	19	dimensional	dimensional	ADJ
ap-7354	39	20	do	do	NOUN
ap-7354	39	21	.	.	PUNCT
ap-7354	40	1	the	the	DET
ap-7354	40	2	experiment	experiment	NOUN
ap-7354	40	3	depends	depend	VERB
ap-7354	40	4	on	on	ADP
ap-7354	40	5	a	a	DET
ap-7354	40	6	relation	relation	NOUN
ap-7354	40	7	of	of	ADP
ap-7354	40	8	the	the	DET
ap-7354	40	9	do	do	NOUN
ap-7354	40	10	to	to	ADP
ap-7354	40	11	a	a	DET
ap-7354	40	12	corresponding	correspond	VERB
ap-7354	40	13	tight	tight	ADV
ap-7354	40	14	-	-	PUNCT
ap-7354	40	15	binding	bind	VERB
ap-7354	40	16	system	system	NOUN
ap-7354	40	17	.	.	PUNCT
ap-7354	41	1	the	the	DET
ap-7354	41	2	experimental	experimental	ADJ
ap-7354	41	3	results	result	NOUN
ap-7354	41	4	obtained	obtain	VERB
ap-7354	41	5	show	show	VERB
ap-7354	41	6	that	that	SCONJ
ap-7354	41	7	the	the	DET
ap-7354	41	8	spectrum	spectrum	NOUN
ap-7354	41	9	of	of	ADP
ap-7354	41	10	the	the	DET
ap-7354	41	11	one	one	NUM
ap-7354	41	12	-	-	PUNCT
ap-7354	41	13	dimensional	dimensional	ADJ
ap-7354	41	14	do	do	NOUN
ap-7354	41	15	is	be	AUX
ap-7354	41	16	in	in	ADP
ap-7354	41	17	good	good	ADJ
ap-7354	41	18	agreement	agreement	NOUN
ap-7354	41	19	with	with	ADP
ap-7354	41	20	that	that	PRON
ap-7354	41	21	of	of	ADP
ap-7354	41	22	the	the	DET
ap-7354	41	23	theory	theory	NOUN
ap-7354	41	24	.	.	PUNCT
ap-7354	42	1	quimbay	quimbay	PROPN
ap-7354	42	2	et	et	PROPN
ap-7354	42	3	al	al	PROPN
ap-7354	42	4	.	.	PUNCT
ap-7354	43	1	[	[	X
ap-7354	43	2	27	27	NUM
ap-7354	43	3	,	,	PUNCT
ap-7354	43	4	28	28	NUM
ap-7354	43	5	]	]	PUNCT
ap-7354	43	6	show	show	VERB
ap-7354	43	7	that	that	SCONJ
ap-7354	43	8	the	the	DET
ap-7354	43	9	do	do	NOUN
ap-7354	43	10	may	may	AUX
ap-7354	43	11	describe	describe	VERB
ap-7354	43	12	a	a	DET
ap-7354	43	13	naturally	naturally	ADV
ap-7354	43	14	occurring	occur	VERB
ap-7354	43	15	physical	physical	ADJ
ap-7354	43	16	system	system	NOUN
ap-7354	43	17	.	.	PUNCT
ap-7354	44	1	more	more	ADV
ap-7354	44	2	precisely	precisely	ADV
ap-7354	44	3	,	,	PUNCT
ap-7354	44	4	that	that	DET
ap-7354	44	5	case	case	NOUN
ap-7354	44	6	of	of	ADP
ap-7354	44	7	a	a	DET
ap-7354	44	8	two	two	NUM
ap-7354	44	9	-	-	PUNCT
ap-7354	44	10	dimensional	dimensional	ADJ
ap-7354	44	11	do	do	NOUN
ap-7354	44	12	can	can	AUX
ap-7354	44	13	be	be	AUX
ap-7354	44	14	used	use	VERB
ap-7354	44	15	to	to	PART
ap-7354	44	16	describe	describe	VERB
ap-7354	44	17	the	the	DET
ap-7354	44	18	dynamics	dynamic	NOUN
ap-7354	44	19	of	of	ADP
ap-7354	44	20	the	the	DET
ap-7354	44	21	charge	charge	NOUN
ap-7354	44	22	carriers	carrier	NOUN
ap-7354	44	23	in	in	ADP
ap-7354	44	24	graphene	graphene	NOUN
ap-7354	44	25	,	,	PUNCT
ap-7354	44	26	and	and	CCONJ
ap-7354	44	27	hence	hence	ADV
ap-7354	44	28	its	its	PRON
ap-7354	44	29	electronic	electronic	ADJ
ap-7354	44	30	properties	property	NOUN
ap-7354	44	31	[	[	X
ap-7354	44	32	29	29	NUM
ap-7354	44	33	]	]	PUNCT
ap-7354	44	34	.	.	PUNCT
ap-7354	45	1	this	this	DET
ap-7354	45	2	paper	paper	NOUN
ap-7354	45	3	is	be	AUX
ap-7354	45	4	organized	organize	VERB
ap-7354	45	5	as	as	SCONJ
ap-7354	45	6	follows	follow	VERB
ap-7354	45	7	.	.	PUNCT
ap-7354	46	1	in	in	ADP
ap-7354	46	2	section	section	NOUN
ap-7354	46	3	2	2	NUM
ap-7354	46	4	,	,	PUNCT
ap-7354	46	5	the	the	DET
ap-7354	46	6	dnc	dnc	PROPN
ap-7354	46	7	geometry	geometry	NOUN
ap-7354	46	8	is	be	AUX
ap-7354	46	9	briefly	briefly	ADV
ap-7354	46	10	reviewed	review	VERB
ap-7354	46	11	.	.	PUNCT
ap-7354	47	1	in	in	ADP
ap-7354	47	2	section	section	NOUN
ap-7354	47	3	3	3	NUM
ap-7354	47	4	,	,	PUNCT
ap-7354	47	5	the	the	DET
ap-7354	47	6	two	two	NUM
ap-7354	47	7	-	-	PUNCT
ap-7354	47	8	dimensional	dimensional	ADJ
ap-7354	47	9	dnc	dnc	PROPN
ap-7354	47	10	do	do	AUX
ap-7354	47	11	is	be	AUX
ap-7354	47	12	investigated	investigate	VERB
ap-7354	47	13	,	,	PUNCT
ap-7354	47	14	where	where	SCONJ
ap-7354	47	15	in	in	ADP
ap-7354	47	16	sub	sub	NOUN
ap-7354	47	17	-	-	NOUN
ap-7354	47	18	section	section	NOUN
ap-7354	47	19	3.2	3.2	NUM
ap-7354	47	20	,	,	PUNCT
ap-7354	47	21	the	the	DET
ap-7354	47	22	energy	energy	NOUN
ap-7354	47	23	spectrum	spectrum	NOUN
ap-7354	47	24	in	in	ADP
ap-7354	47	25	nc	nc	PROPN
ap-7354	47	26	space	space	NOUN
ap-7354	47	27	is	be	AUX
ap-7354	47	28	obtained	obtain	VERB
ap-7354	47	29	.	.	PUNCT
ap-7354	48	1	in	in	ADP
ap-7354	48	2	sub	sub	NOUN
ap-7354	48	3	-	-	NOUN
ap-7354	48	4	section	section	NOUN
ap-7354	48	5	3.3	3.3	NUM
ap-7354	48	6	,	,	PUNCT
ap-7354	48	7	based	base	VERB
ap-7354	48	8	on	on	ADP
ap-7354	48	9	the	the	DET
ap-7354	48	10	perturbation	perturbation	NOUN
ap-7354	48	11	theory	theory	NOUN
ap-7354	48	12	and	and	CCONJ
ap-7354	48	13	fock	fock	ADJ
ap-7354	48	14	basis	basis	NOUN
ap-7354	48	15	,	,	PUNCT
ap-7354	48	16	the	the	DET
ap-7354	48	17	energy	energy	NOUN
ap-7354	48	18	spectrum	spectrum	NOUN
ap-7354	48	19	including	include	VERB
ap-7354	48	20	the	the	DET
ap-7354	48	21	dynamical	dynamical	ADJ
ap-7354	48	22	noncommutativity	noncommutativity	NOUN
ap-7354	48	23	effect	effect	NOUN
ap-7354	48	24	is	be	AUX
ap-7354	48	25	obtained	obtain	VERB
ap-7354	48	26	,	,	PUNCT
ap-7354	48	27	therefore	therefore	ADV
ap-7354	48	28	,	,	PUNCT
ap-7354	48	29	we	we	PRON
ap-7354	48	30	summarize	summarize	VERB
ap-7354	48	31	the	the	DET
ap-7354	48	32	results	result	NOUN
ap-7354	48	33	and	and	CCONJ
ap-7354	48	34	discussions	discussion	NOUN
ap-7354	48	35	.	.	PUNCT
ap-7354	49	1	section	section	NOUN
ap-7354	49	2	4	4	NUM
ap-7354	49	3	,	,	PUNCT
ap-7354	49	4	is	be	AUX
ap-7354	49	5	then	then	ADV
ap-7354	49	6	devoted	devote	VERB
ap-7354	49	7	to	to	ADP
ap-7354	49	8	the	the	DET
ap-7354	49	9	conclusions	conclusion	NOUN
ap-7354	49	10	.	.	PUNCT
ap-7354	50	1	2	2	X
ap-7354	50	2	.	.	X
ap-7354	50	3	review	review	NOUN
ap-7354	50	4	of	of	ADP
ap-7354	50	5	dynamical	dynamical	ADJ
ap-7354	50	6	noncommutativity	noncommutativity	NOUN
ap-7354	50	7	let	let	VERB
ap-7354	50	8	us	we	PRON
ap-7354	50	9	present	present	VERB
ap-7354	50	10	the	the	DET
ap-7354	50	11	essential	essential	ADJ
ap-7354	50	12	formulas	formula	NOUN
ap-7354	50	13	of	of	ADP
ap-7354	50	14	the	the	DET
ap-7354	50	15	dnc	dnc	PROPN
ap-7354	50	16	space	space	NOUN
ap-7354	50	17	algebra	algebra	NOUN
ap-7354	50	18	we	we	PRON
ap-7354	50	19	need	need	VERB
ap-7354	50	20	in	in	ADP
ap-7354	50	21	this	this	DET
ap-7354	50	22	study	study	NOUN
ap-7354	50	23	.	.	PUNCT
ap-7354	51	1	as	as	SCONJ
ap-7354	51	2	is	be	AUX
ap-7354	51	3	known	know	VERB
ap-7354	51	4	,	,	PUNCT
ap-7354	51	5	at	at	ADP
ap-7354	51	6	the	the	DET
ap-7354	51	7	tiny	tiny	ADJ
ap-7354	51	8	scale	scale	NOUN
ap-7354	51	9	(	(	PUNCT
ap-7354	51	10	string	string	NOUN
ap-7354	51	11	scale	scale	NOUN
ap-7354	51	12	)	)	PUNCT
ap-7354	51	13	,	,	PUNCT
ap-7354	51	14	the	the	DET
ap-7354	51	15	position	position	NOUN
ap-7354	51	16	coordinates	coordinate	NOUN
ap-7354	51	17	do	do	AUX
ap-7354	51	18	not	not	PART
ap-7354	51	19	commute	commute	VERB
ap-7354	51	20	with	with	ADP
ap-7354	51	21	each	each	DET
ap-7354	51	22	other	other	ADJ
ap-7354	51	23	,	,	PUNCT
ap-7354	51	24	thus	thus	ADV
ap-7354	51	25	the	the	DET
ap-7354	51	26	canonical	canonical	ADJ
ap-7354	51	27	variables	variable	NOUN
ap-7354	51	28	satisfy	satisfy	VERB
ap-7354	51	29	the	the	DET
ap-7354	51	30	following	follow	VERB
ap-7354	51	31	deformed	deform	VERB
ap-7354	51	32	heisenberg	heisenberg	PROPN
ap-7354	51	33	commutation	commutation	NOUN
ap-7354	51	34	relation	relation	NOUN
ap-7354	51	35	[	[	PUNCT
ap-7354	51	36	xnc	xnc	PROPN
ap-7354	51	37	µ	µ	X
ap-7354	51	38	,	,	PUNCT
ap-7354	51	39	xnc	xnc	PROPN
ap-7354	51	40	ν	ν	X
ap-7354	51	41	]	]	X
ap-7354	51	42	=	=	SYM
ap-7354	51	43	iθµν	iθµν	NOUN
ap-7354	51	44	,	,	PUNCT
ap-7354	51	45	(	(	PUNCT
ap-7354	51	46	1	1	X
ap-7354	51	47	)	)	PUNCT
ap-7354	51	48	with	with	ADP
ap-7354	51	49	θµν	θµν	NOUN
ap-7354	51	50	being	be	AUX
ap-7354	51	51	an	an	DET
ap-7354	51	52	anti	anti	ADJ
ap-7354	51	53	-	-	ADJ
ap-7354	51	54	symmetric	symmetric	ADJ
ap-7354	51	55	tensor	tensor	NOUN
ap-7354	51	56	.	.	PUNCT
ap-7354	52	1	in	in	ADP
ap-7354	52	2	simplest	simple	ADJ
ap-7354	52	3	way	way	NOUN
ap-7354	52	4	,	,	PUNCT
ap-7354	52	5	the	the	DET
ap-7354	52	6	deformation	deformation	NOUN
ap-7354	52	7	parameter	parameter	NOUN
ap-7354	52	8	is	be	AUX
ap-7354	52	9	considered	consider	VERB
ap-7354	52	10	a	a	DET
ap-7354	52	11	real	real	ADV
ap-7354	52	12	constant	constant	ADJ
ap-7354	52	13	.	.	PUNCT
ap-7354	53	1	but	but	CCONJ
ap-7354	53	2	,	,	PUNCT
ap-7354	53	3	in	in	ADP
ap-7354	53	4	general	general	ADJ
ap-7354	53	5	,	,	PUNCT
ap-7354	53	6	θµν	θµν	PRON
ap-7354	53	7	can	can	AUX
ap-7354	53	8	be	be	AUX
ap-7354	53	9	a	a	DET
ap-7354	53	10	function	function	NOUN
ap-7354	53	11	of	of	ADP
ap-7354	53	12	coordinates	coordinate	NOUN
ap-7354	53	13	.	.	PUNCT
ap-7354	54	1	fring	fre	VERB
ap-7354	54	2	et	et	PROPN
ap-7354	54	3	al	al	PROPN
ap-7354	54	4	.	.	PUNCT
ap-7354	55	1	[	[	X
ap-7354	55	2	16	16	NUM
ap-7354	55	3	]	]	PUNCT
ap-7354	55	4	made	make	VERB
ap-7354	55	5	a	a	DET
ap-7354	55	6	generalization	generalization	NOUN
ap-7354	55	7	of	of	ADP
ap-7354	55	8	an	an	DET
ap-7354	55	9	nc	nc	PROPN
ap-7354	55	10	space	space	NOUN
ap-7354	55	11	to	to	ADP
ap-7354	55	12	a	a	DET
ap-7354	55	13	position	position	NOUN
ap-7354	55	14	-	-	PUNCT
ap-7354	55	15	dependent	dependent	ADJ
ap-7354	55	16	space	space	NOUN
ap-7354	55	17	by	by	ADP
ap-7354	55	18	introducing	introduce	VERB
ap-7354	55	19	a	a	DET
ap-7354	55	20	set	set	NOUN
ap-7354	55	21	of	of	ADP
ap-7354	55	22	new	new	ADJ
ap-7354	55	23	variables	variable	NOUN
ap-7354	55	24	x	x	NOUN
ap-7354	55	25	,	,	PUNCT
ap-7354	55	26	y	y	PROPN
ap-7354	55	27	,	,	PUNCT
ap-7354	55	28	px	px	PROPN
ap-7354	55	29	,	,	PUNCT
ap-7354	55	30	py	py	PROPN
ap-7354	55	31	and	and	CCONJ
ap-7354	55	32	converting	convert	VERB
ap-7354	55	33	the	the	DET
ap-7354	55	34	constant	constant	ADJ
ap-7354	55	35	θ	θ	NOUN
ap-7354	55	36	into	into	ADP
ap-7354	55	37	a	a	DET
ap-7354	55	38	function	function	NOUN
ap-7354	55	39	of	of	ADP
ap-7354	55	40	coordinates	coordinate	NOUN
ap-7354	55	41	θ(x	θ(x	PROPN
ap-7354	55	42	,	,	PUNCT
ap-7354	55	43	y	y	PROPN
ap-7354	55	44	)	)	PUNCT
ap-7354	56	1	=	=	SYM
ap-7354	56	2	θ	θ	NOUN
ap-7354	56	3	(	(	PUNCT
ap-7354	56	4	1	1	NUM
ap-7354	56	5	+	+	CCONJ
ap-7354	56	6	τy	τy	NUM
ap-7354	56	7	2	2	NUM
ap-7354	56	8	)	)	PUNCT
ap-7354	56	9	.	.	PUNCT
ap-7354	57	1	as	as	ADP
ap-7354	57	2	another	another	DET
ap-7354	57	3	example	example	NOUN
ap-7354	57	4	of	of	ADP
ap-7354	57	5	θ(x	θ(x	PROPN
ap-7354	57	6	,	,	PUNCT
ap-7354	57	7	y	y	PROPN
ap-7354	57	8	)	)	PUNCT
ap-7354	57	9	,	,	PUNCT
ap-7354	57	10	we	we	PRON
ap-7354	57	11	also	also	ADV
ap-7354	57	12	mention	mention	VERB
ap-7354	57	13	that	that	SCONJ
ap-7354	57	14	gomes	gome	NOUN
ap-7354	57	15	et	et	PROPN
ap-7354	57	16	al	al	PROPN
ap-7354	57	17	.	.	PUNCT
ap-7354	58	1	[	[	X
ap-7354	58	2	17	17	NUM
ap-7354	58	3	]	]	AUX
ap-7354	58	4	chose	choose	VERB
ap-7354	58	5	in	in	ADP
ap-7354	58	6	their	their	PRON
ap-7354	58	7	study	study	NOUN
ap-7354	58	8	θ(x	θ(x	PROPN
ap-7354	58	9	,	,	PUNCT
ap-7354	58	10	y	y	PROPN
ap-7354	58	11	)	)	PUNCT
ap-7354	59	1	=	=	NOUN
ap-7354	59	2	θ/[1	θ/[1	NOUN
ap-7354	59	3	+	+	CCONJ
ap-7354	59	4	θα	θα	ADP
ap-7354	59	5	(	(	PUNCT
ap-7354	59	6	1	1	NUM
ap-7354	59	7	+	+	NUM
ap-7354	59	8	y	y	PROPN
ap-7354	59	9	2	2	NUM
ap-7354	59	10	)	)	PUNCT
ap-7354	59	11	]	]	PUNCT
ap-7354	59	12	.	.	PUNCT
ap-7354	60	1	however	however	ADV
ap-7354	60	2	,	,	PUNCT
ap-7354	60	3	as	as	ADP
ap-7354	60	4	a	a	DET
ap-7354	60	5	deformation	deformation	NOUN
ap-7354	60	6	of	of	ADP
ap-7354	60	7	this	this	DET
ap-7354	60	8	nc	nc	PROPN
ap-7354	60	9	parameter	parameter	PROPN
ap-7354	60	10	form	form	NOUN
ap-7354	60	11	will	will	AUX
ap-7354	60	12	almost	almost	ADV
ap-7354	60	13	inevitably	inevitably	ADV
ap-7354	60	14	lead	lead	VERB
ap-7354	60	15	to	to	ADP
ap-7354	60	16	non	non	ADJ
ap-7354	60	17	-	-	ADJ
ap-7354	60	18	hermitian	hermitian	ADJ
ap-7354	60	19	coordinates	coordinate	NOUN
ap-7354	60	20	,	,	PUNCT
ap-7354	60	21	it	it	PRON
ap-7354	60	22	was	be	AUX
ap-7354	60	23	pointed	point	VERB
ap-7354	60	24	out	out	ADP
ap-7354	60	25	[	[	X
ap-7354	60	26	30	30	NUM
ap-7354	60	27	]	]	PUNCT
ap-7354	60	28	that	that	SCONJ
ap-7354	60	29	these	these	DET
ap-7354	60	30	types	type	NOUN
ap-7354	60	31	of	of	ADP
ap-7354	60	32	structures	structure	NOUN
ap-7354	60	33	are	be	AUX
ap-7354	60	34	related	relate	VERB
ap-7354	60	35	directly	directly	ADV
ap-7354	60	36	to	to	ADP
ap-7354	60	37	non	non	ADJ
ap-7354	60	38	-	-	ADJ
ap-7354	60	39	hermitian	hermitian	ADJ
ap-7354	60	40	hamiltonian	hamiltonian	ADJ
ap-7354	60	41	systems	system	NOUN
ap-7354	60	42	.	.	PUNCT
ap-7354	61	1	later	later	ADV
ap-7354	61	2	,	,	PUNCT
ap-7354	61	3	it	it	PRON
ap-7354	61	4	is	be	AUX
ap-7354	61	5	explained	explain	VERB
ap-7354	61	6	how	how	SCONJ
ap-7354	61	7	this	this	DET
ap-7354	61	8	problem	problem	NOUN
ap-7354	61	9	was	be	AUX
ap-7354	61	10	solved	solve	VERB
ap-7354	61	11	.	.	PUNCT
ap-7354	62	1	in	in	ADP
ap-7354	62	2	the	the	DET
ap-7354	62	3	new	new	ADJ
ap-7354	62	4	type	type	NOUN
ap-7354	62	5	of	of	ADP
ap-7354	62	6	the	the	DET
ap-7354	62	7	two	two	NUM
ap-7354	62	8	-	-	PUNCT
ap-7354	62	9	dimensional	dimensional	ADJ
ap-7354	62	10	nc	nc	PROPN
ap-7354	62	11	space	space	NOUN
ap-7354	62	12	,	,	PUNCT
ap-7354	62	13	which	which	PRON
ap-7354	62	14	is	be	AUX
ap-7354	62	15	known	know	VERB
ap-7354	62	16	as	as	ADP
ap-7354	62	17	the	the	DET
ap-7354	62	18	dnc	dnc	PROPN
ap-7354	62	19	space	space	NOUN
ap-7354	62	20	or	or	CCONJ
ap-7354	62	21	τ−space	τ−space	NOUN
ap-7354	62	22	,	,	PUNCT
ap-7354	62	23	the	the	DET
ap-7354	62	24	commutation	commutation	NOUN
ap-7354	62	25	relations	relation	NOUN
ap-7354	62	26	are	be	AUX
ap-7354	62	27	[	[	X
ap-7354	62	28	16	16	NUM
ap-7354	62	29	]	]	PUNCT
ap-7354	63	1	[	[	X
ap-7354	63	2	x	x	X
ap-7354	63	3	,	,	PUNCT
ap-7354	63	4	y	y	PROPN
ap-7354	63	5	]	]	PUNCT
ap-7354	63	6	=	=	PUNCT
ap-7354	63	7	iθ	iθ	NOUN
ap-7354	63	8	(	(	PUNCT
ap-7354	63	9	1	1	NUM
ap-7354	63	10	+	+	CCONJ
ap-7354	63	11	τy	τy	NUM
ap-7354	63	12	2	2	NUM
ap-7354	63	13	)	)	PUNCT
ap-7354	63	14	,	,	PUNCT
ap-7354	64	1	[	[	X
ap-7354	64	2	y	y	NOUN
ap-7354	64	3	,	,	PUNCT
ap-7354	64	4	py	py	X
ap-7354	64	5	]	]	X
ap-7354	64	6	=	=	SYM
ap-7354	64	7	iℏ	iℏ	NOUN
ap-7354	64	8	(	(	PUNCT
ap-7354	64	9	1	1	NUM
ap-7354	64	10	+	+	CCONJ
ap-7354	64	11	τy	τy	NUM
ap-7354	64	12	2	2	NUM
ap-7354	64	13	)	)	PUNCT
ap-7354	64	14	,	,	PUNCT
ap-7354	65	1	[	[	X
ap-7354	65	2	x	x	X
ap-7354	65	3	,	,	PUNCT
ap-7354	65	4	px	px	X
ap-7354	65	5	]	]	X
ap-7354	65	6	=	=	SYM
ap-7354	65	7	iℏ	iℏ	NOUN
ap-7354	65	8	(	(	PUNCT
ap-7354	65	9	1	1	NUM
ap-7354	65	10	+	+	CCONJ
ap-7354	65	11	τy	τy	NUM
ap-7354	65	12	2	2	NUM
ap-7354	65	13	)	)	PUNCT
ap-7354	65	14	,	,	PUNCT
ap-7354	66	1	[	[	X
ap-7354	66	2	y	y	X
ap-7354	66	3	,	,	PUNCT
ap-7354	66	4	px	px	X
ap-7354	66	5	]	]	X
ap-7354	66	6	=	=	SYM
ap-7354	66	7	0	0	NUM
ap-7354	66	8	,	,	PUNCT
ap-7354	66	9	[	[	X
ap-7354	66	10	x	x	X
ap-7354	66	11	,	,	PUNCT
ap-7354	66	12	py	py	X
ap-7354	66	13	]	]	X
ap-7354	66	14	=	=	SYM
ap-7354	66	15	2iτy	2iτy	NUM
ap-7354	66	16	(	(	PUNCT
ap-7354	66	17	θpy	θpy	NOUN
ap-7354	66	18	+	+	CCONJ
ap-7354	66	19	ℏx	ℏx	X
ap-7354	66	20	)	)	PUNCT
ap-7354	66	21	,	,	PUNCT
ap-7354	67	1	[	[	X
ap-7354	67	2	px	px	X
ap-7354	67	3	,	,	PUNCT
ap-7354	67	4	py	py	X
ap-7354	67	5	]	]	X
ap-7354	67	6	=	=	SYM
ap-7354	67	7	0	0	X
ap-7354	67	8	.	.	PUNCT
ap-7354	68	1	(	(	PUNCT
ap-7354	68	2	2	2	X
ap-7354	68	3	)	)	PUNCT
ap-7354	68	4	it	it	PRON
ap-7354	68	5	is	be	AUX
ap-7354	68	6	interesting	interesting	ADJ
ap-7354	68	7	to	to	PART
ap-7354	68	8	note	note	VERB
ap-7354	68	9	that	that	SCONJ
ap-7354	69	1	√	√	NUM
ap-7354	69	2	θ	θ	PROPN
ap-7354	69	3	and	and	CCONJ
ap-7354	69	4	√	√	PROPN
ap-7354	69	5	τ	τ	PROPN
ap-7354	69	6	have	have	VERB
ap-7354	69	7	dimensions	dimension	NOUN
ap-7354	69	8	of	of	ADP
ap-7354	69	9	l	l	NOUN
ap-7354	69	10	and	and	CCONJ
ap-7354	69	11	l−1	l−1	PROPN
ap-7354	69	12	,	,	PUNCT
ap-7354	69	13	respectively	respectively	ADV
ap-7354	69	14	.	.	PUNCT
ap-7354	70	1	in	in	ADP
ap-7354	70	2	the	the	DET
ap-7354	70	3	limit	limit	NOUN
ap-7354	70	4	τ	τ	X
ap-7354	70	5	→	→	SYM
ap-7354	70	6	0	0	NUM
ap-7354	70	7	,	,	PUNCT
ap-7354	70	8	we	we	PRON
ap-7354	70	9	obtain	obtain	VERB
ap-7354	70	10	the	the	DET
ap-7354	70	11	following	follow	VERB
ap-7354	70	12	non	non	ADJ
ap-7354	70	13	-	-	ADJ
ap-7354	70	14	dynamical	dynamical	ADJ
ap-7354	70	15	nc	nc	PROPN
ap-7354	70	16	commutation	commutation	NOUN
ap-7354	70	17	relations	relation	NOUN
ap-7354	70	18	[	[	X
ap-7354	70	19	xnc	xnc	PROPN
ap-7354	70	20	,	,	PUNCT
ap-7354	70	21	ync	ync	NOUN
ap-7354	70	22	]	]	X
ap-7354	70	23	=	=	PUNCT
ap-7354	70	24	iθ	iθ	NOUN
ap-7354	70	25	,	,	PUNCT
ap-7354	70	26	[	[	PUNCT
ap-7354	70	27	ync	ync	PROPN
ap-7354	70	28	,	,	PUNCT
ap-7354	70	29	pnc	pnc	PROPN
ap-7354	70	30	y	y	PROPN
ap-7354	70	31	]	]	PUNCT
ap-7354	71	1	=	=	PUNCT
ap-7354	71	2	iℏ	iℏ	NOUN
ap-7354	71	3	,	,	PUNCT
ap-7354	71	4	[	[	X
ap-7354	71	5	xnc	xnc	PROPN
ap-7354	71	6	,	,	PUNCT
ap-7354	71	7	pnc	pnc	PROPN
ap-7354	71	8	x	x	X
ap-7354	71	9	]	]	X
ap-7354	71	10	=	=	PUNCT
ap-7354	71	11	iℏ	iℏ	NOUN
ap-7354	71	12	,	,	PUNCT
ap-7354	71	13	[	[	X
ap-7354	71	14	ync	ync	NOUN
ap-7354	71	15	,	,	PUNCT
ap-7354	71	16	pnc	pnc	PROPN
ap-7354	71	17	x	x	X
ap-7354	71	18	]	]	X
ap-7354	71	19	=	=	PUNCT
ap-7354	71	20	0	0	NUM
ap-7354	71	21	,	,	PUNCT
ap-7354	71	22	[	[	PUNCT
ap-7354	71	23	xnc	xnc	PROPN
ap-7354	71	24	,	,	PUNCT
ap-7354	71	25	pnc	pnc	PROPN
ap-7354	71	26	y	y	PROPN
ap-7354	71	27	]	]	PUNCT
ap-7354	71	28	=	=	PUNCT
ap-7354	71	29	0	0	NUM
ap-7354	71	30	,	,	PUNCT
ap-7354	71	31	[	[	PUNCT
ap-7354	71	32	pnc	pnc	X
ap-7354	71	33	x	x	X
ap-7354	71	34	,	,	PUNCT
ap-7354	71	35	pnc	pnc	PROPN
ap-7354	71	36	y	y	PROPN
ap-7354	71	37	]	]	PUNCT
ap-7354	71	38	=	=	PUNCT
ap-7354	71	39	0	0	X
ap-7354	71	40	.	.	PUNCT
ap-7354	71	41	(	(	PUNCT
ap-7354	71	42	3	3	X
ap-7354	71	43	)	)	PUNCT
ap-7354	71	44	the	the	DET
ap-7354	71	45	coordinate	coordinate	NOUN
ap-7354	71	46	x	x	PUNCT
ap-7354	71	47	and	and	CCONJ
ap-7354	71	48	the	the	DET
ap-7354	71	49	momentum	momentum	NOUN
ap-7354	71	50	py	py	PROPN
ap-7354	71	51	are	be	AUX
ap-7354	71	52	not	not	PART
ap-7354	71	53	hermitian	hermitian	ADJ
ap-7354	71	54	,	,	PUNCT
ap-7354	71	55	which	which	PRON
ap-7354	71	56	makes	make	VERB
ap-7354	71	57	the	the	DET
ap-7354	71	58	hamiltonian	hamiltonian	NOUN
ap-7354	71	59	that	that	PRON
ap-7354	71	60	includes	include	VERB
ap-7354	71	61	these	these	DET
ap-7354	71	62	variables	variable	NOUN
ap-7354	71	63	non	non	ADJ
ap-7354	71	64	-	-	ADJ
ap-7354	71	65	hermitian	hermitian	ADJ
ap-7354	71	66	.	.	PUNCT
ap-7354	72	1	we	we	PRON
ap-7354	72	2	represent	represent	VERB
ap-7354	72	3	algebra	algebra	NOUN
ap-7354	72	4	(	(	PUNCT
ap-7354	72	5	2	2	NUM
ap-7354	72	6	)	)	PUNCT
ap-7354	72	7	in	in	ADP
ap-7354	72	8	terms	term	NOUN
ap-7354	72	9	of	of	ADP
ap-7354	72	10	the	the	DET
ap-7354	72	11	standard	standard	PROPN
ap-7354	72	12	hermitian	hermitian	PROPN
ap-7354	72	13	nc	nc	PROPN
ap-7354	72	14	variable	variable	PROPN
ap-7354	72	15	operators	operator	NOUN
ap-7354	72	16	xnc	xnc	PROPN
ap-7354	72	17	,	,	PUNCT
ap-7354	72	18	ync	ync	PROPN
ap-7354	72	19	,	,	PUNCT
ap-7354	72	20	pnc	pnc	PROPN
ap-7354	72	21	x	x	PROPN
ap-7354	72	22	,	,	PUNCT
ap-7354	72	23	pnc	pnc	PROPN
ap-7354	72	24	y	y	PROPN
ap-7354	72	25	as	as	ADP
ap-7354	72	26	x	x	X
ap-7354	72	27	=	=	PRON
ap-7354	72	28	(	(	PUNCT
ap-7354	72	29	1	1	NUM
ap-7354	72	30	+	+	CCONJ
ap-7354	72	31	τ	τ	X
ap-7354	72	32	(	(	PUNCT
ap-7354	72	33	ync)2	ync)2	PROPN
ap-7354	72	34	)	)	PUNCT
ap-7354	72	35	xnc	xnc	PROPN
ap-7354	72	36	,	,	PUNCT
ap-7354	72	37	y	y	PROPN
ap-7354	72	38	=	=	SYM
ap-7354	72	39	ync	ync	PROPN
ap-7354	72	40	,	,	PUNCT
ap-7354	72	41	py	py	PROPN
ap-7354	72	42	=	=	PUNCT
ap-7354	72	43	(	(	PUNCT
ap-7354	72	44	1	1	NUM
ap-7354	72	45	+	+	CCONJ
ap-7354	72	46	τ	τ	X
ap-7354	72	47	(	(	PUNCT
ap-7354	72	48	ync)2	ync)2	PROPN
ap-7354	72	49	)	)	PUNCT
ap-7354	72	50	pnc	pnc	PROPN
ap-7354	72	51	y	y	PROPN
ap-7354	72	52	,	,	PUNCT
ap-7354	72	53	px	px	PROPN
ap-7354	72	54	=	=	PUNCT
ap-7354	72	55	pnc	pnc	PROPN
ap-7354	72	56	x	x	X
ap-7354	72	57	.	.	PUNCT
ap-7354	73	1	(	(	PUNCT
ap-7354	73	2	4	4	NUM
ap-7354	73	3	)	)	PUNCT
ap-7354	73	4	from	from	ADP
ap-7354	73	5	this	this	DET
ap-7354	73	6	representation	representation	NOUN
ap-7354	73	7	,	,	PUNCT
ap-7354	73	8	we	we	PRON
ap-7354	73	9	can	can	AUX
ap-7354	73	10	see	see	VERB
ap-7354	73	11	that	that	SCONJ
ap-7354	73	12	some	some	PRON
ap-7354	73	13	of	of	ADP
ap-7354	73	14	the	the	DET
ap-7354	73	15	operators	operator	NOUN
ap-7354	73	16	involved	involve	VERB
ap-7354	73	17	above	above	ADV
ap-7354	73	18	are	be	AUX
ap-7354	73	19	no	no	ADV
ap-7354	73	20	longer	long	ADV
ap-7354	73	21	hermitian	hermitian	ADJ
ap-7354	73	22	.	.	PUNCT
ap-7354	74	1	however	however	ADV
ap-7354	74	2	,	,	PUNCT
ap-7354	74	3	to	to	PART
ap-7354	74	4	convert	convert	VERB
ap-7354	74	5	the	the	DET
ap-7354	74	6	non	non	ADJ
ap-7354	74	7	-	-	ADJ
ap-7354	74	8	hermitian	hermitian	ADJ
ap-7354	74	9	variables	variable	NOUN
ap-7354	74	10	into	into	ADP
ap-7354	74	11	a	a	DET
ap-7354	74	12	hermitian	hermitian	ADJ
ap-7354	74	13	one	one	NOUN
ap-7354	74	14	,	,	PUNCT
ap-7354	74	15	we	we	PRON
ap-7354	74	16	use	use	VERB
ap-7354	74	17	a	a	DET
ap-7354	74	18	similarity	similarity	NOUN
ap-7354	74	19	transformation	transformation	NOUN
ap-7354	74	20	as	as	ADP
ap-7354	74	21	a	a	DET
ap-7354	74	22	dyson	dyson	NOUN
ap-7354	74	23	map	map	NOUN
ap-7354	74	24	ηoη−1	ηoη−1	PROPN
ap-7354	74	25	=	=	PUNCT
ap-7354	74	26	o	o	PROPN
ap-7354	75	1	=	=	PUNCT
ap-7354	75	2	o†	o†	ADJ
ap-7354	75	3	with	with	ADP
ap-7354	75	4	η	η	PROPN
ap-7354	75	5	=	=	PROPN
ap-7354	75	6	(	(	PUNCT
ap-7354	75	7	1+τy	1+τy	NUM
ap-7354	75	8	2)−	2)−	NUM
ap-7354	75	9	1	1	NUM
ap-7354	75	10	2	2	NUM
ap-7354	75	11	,	,	PUNCT
ap-7354	75	12	as	as	SCONJ
ap-7354	75	13	stated	state	VERB
ap-7354	75	14	in	in	ADP
ap-7354	75	15	[	[	X
ap-7354	75	16	16	16	NUM
ap-7354	75	17	]	]	PUNCT
ap-7354	75	18	.	.	PUNCT
ap-7354	76	1	therefore	therefore	ADV
ap-7354	76	2	,	,	PUNCT
ap-7354	76	3	we	we	PRON
ap-7354	76	4	express	express	VERB
ap-7354	76	5	the	the	DET
ap-7354	76	6	new	new	ADJ
ap-7354	76	7	hermitian	hermitian	ADJ
ap-7354	76	8	variables	variable	NOUN
ap-7354	76	9	x	x	NOUN
ap-7354	76	10	,	,	PUNCT
ap-7354	76	11	y	y	PROPN
ap-7354	76	12	,	,	PUNCT
ap-7354	76	13	px	px	PROPN
ap-7354	76	14	and	and	CCONJ
ap-7354	76	15	py	py	PROPN
ap-7354	76	16	in	in	ADP
ap-7354	76	17	terms	term	NOUN
ap-7354	76	18	of	of	ADP
ap-7354	76	19	nc	nc	PROPN
ap-7354	76	20	variables	variable	NOUN
ap-7354	76	21	as	as	SCONJ
ap-7354	76	22	follows	follow	VERB
ap-7354	76	23	690	690	NUM
ap-7354	76	24	vol	vol	NOUN
ap-7354	76	25	.	.	PUNCT
ap-7354	77	1	61	61	NUM
ap-7354	77	2	no	no	NOUN
ap-7354	77	3	.	.	PUNCT
ap-7354	78	1	6/2021	6/2021	NUM
ap-7354	78	2	dirac	dirac	NOUN
ap-7354	78	3	oscillator	oscillator	NOUN
ap-7354	78	4	in	in	ADP
ap-7354	78	5	dynamical	dynamical	ADJ
ap-7354	78	6	noncommutative	noncommutative	ADJ
ap-7354	78	7	space	space	NOUN
ap-7354	78	8	x	x	X
ap-7354	79	1	=	=	PUNCT
ap-7354	79	2	ηxη−1	ηxη−1	PROPN
ap-7354	79	3	=	=	PUNCT
ap-7354	79	4	(	(	PUNCT
ap-7354	79	5	1	1	NUM
ap-7354	79	6	+	+	CCONJ
ap-7354	79	7	τy	τy	NUM
ap-7354	79	8	2)−	2)−	NUM
ap-7354	79	9	1	1	NUM
ap-7354	79	10	2x(1	2x(1	NUM
ap-7354	79	11	+	+	CCONJ
ap-7354	79	12	τy	τy	NUM
ap-7354	79	13	2	2	NUM
ap-7354	79	14	)	)	PUNCT
ap-7354	79	15	1	1	NUM
ap-7354	79	16	2	2	NUM
ap-7354	79	17	=	=	SYM
ap-7354	79	18	(	(	PUNCT
ap-7354	79	19	1	1	NUM
ap-7354	79	20	+	+	NUM
ap-7354	79	21	τ	τ	PROPN
ap-7354	79	22	(	(	PUNCT
ap-7354	79	23	ync)2	ync)2	PROPN
ap-7354	79	24	)	)	PUNCT
ap-7354	79	25	1	1	NUM
ap-7354	79	26	2xnc(1	2xnc(1	NUM
ap-7354	79	27	+	+	CCONJ
ap-7354	79	28	τ	τ	PROPN
ap-7354	79	29	(	(	PUNCT
ap-7354	79	30	ync)2	ync)2	PROPN
ap-7354	79	31	)	)	PUNCT
ap-7354	79	32	1	1	NUM
ap-7354	79	33	2	2	NUM
ap-7354	79	34	,	,	PUNCT
ap-7354	79	35	y	y	NOUN
ap-7354	79	36	=	=	PUNCT
ap-7354	79	37	ηy	ηy	PROPN
ap-7354	79	38	η−1	η−1	PROPN
ap-7354	79	39	=	=	PUNCT
ap-7354	79	40	(	(	PUNCT
ap-7354	79	41	1	1	NUM
ap-7354	79	42	+	+	CCONJ
ap-7354	79	43	τ	τ	PROPN
ap-7354	79	44	(	(	PUNCT
ap-7354	79	45	ync)2)−	ync)2)−	ADJ
ap-7354	79	46	1	1	NUM
ap-7354	79	47	2	2	NUM
ap-7354	79	48	ync(1	ync(1	NOUN
ap-7354	79	49	+	+	X
ap-7354	79	50	τ	τ	PROPN
ap-7354	79	51	(	(	PUNCT
ap-7354	79	52	ync)2	ync)2	PROPN
ap-7354	79	53	)	)	PUNCT
ap-7354	79	54	1	1	NUM
ap-7354	79	55	2	2	NUM
ap-7354	79	56	=	=	SYM
ap-7354	79	57	ync	ync	NOUN
ap-7354	79	58	,	,	PUNCT
ap-7354	79	59	px	px	PROPN
ap-7354	79	60	=	=	PUNCT
ap-7354	79	61	ηpxη	ηpxη	NOUN
ap-7354	79	62	−1	−1	NOUN
ap-7354	79	63	=	=	SYM
ap-7354	79	64	(	(	PUNCT
ap-7354	79	65	1	1	NUM
ap-7354	79	66	+	+	CCONJ
ap-7354	79	67	τ	τ	PROPN
ap-7354	79	68	(	(	PUNCT
ap-7354	79	69	ync)2)−	ync)2)−	ADJ
ap-7354	79	70	1	1	NUM
ap-7354	79	71	2	2	NUM
ap-7354	79	72	pnc	pnc	NOUN
ap-7354	79	73	x	x	SYM
ap-7354	79	74	(	(	PUNCT
ap-7354	79	75	1	1	NUM
ap-7354	79	76	+	+	NUM
ap-7354	79	77	τ	τ	X
ap-7354	79	78	(	(	PUNCT
ap-7354	79	79	ync)2	ync)2	PROPN
ap-7354	79	80	)	)	PUNCT
ap-7354	79	81	1	1	NUM
ap-7354	79	82	2	2	NUM
ap-7354	79	83	=	=	SYM
ap-7354	79	84	pnc	pnc	X
ap-7354	79	85	x	x	NOUN
ap-7354	79	86	,	,	PUNCT
ap-7354	79	87	py	py	PROPN
ap-7354	79	88	=	=	PUNCT
ap-7354	79	89	ηpyη	ηpyη	PROPN
ap-7354	79	90	−1	−1	NOUN
ap-7354	80	1	=	=	PUNCT
ap-7354	81	1	(	(	PUNCT
ap-7354	81	2	1	1	NUM
ap-7354	81	3	+	+	CCONJ
ap-7354	81	4	τ	τ	PROPN
ap-7354	81	5	(	(	PUNCT
ap-7354	81	6	ync)2)−	ync)2)−	ADJ
ap-7354	81	7	1	1	NUM
ap-7354	81	8	2py(1	2py(1	PROPN
ap-7354	81	9	+	+	NUM
ap-7354	81	10	τ	τ	X
ap-7354	81	11	(	(	PUNCT
ap-7354	81	12	ync)2	ync)2	PROPN
ap-7354	81	13	)	)	PUNCT
ap-7354	81	14	1	1	NUM
ap-7354	81	15	2	2	NUM
ap-7354	81	16	=	=	SYM
ap-7354	81	17	(	(	PUNCT
ap-7354	81	18	1	1	NUM
ap-7354	81	19	+	+	NUM
ap-7354	81	20	τ	τ	PROPN
ap-7354	81	21	(	(	PUNCT
ap-7354	81	22	ync)2	ync)2	PROPN
ap-7354	81	23	)	)	PUNCT
ap-7354	81	24	1	1	NUM
ap-7354	81	25	2	2	NUM
ap-7354	81	26	pnc	pnc	NOUN
ap-7354	81	27	y	y	PROPN
ap-7354	81	28	(	(	PUNCT
ap-7354	81	29	1	1	NUM
ap-7354	81	30	+	+	CCONJ
ap-7354	81	31	τ	τ	PROPN
ap-7354	81	32	(	(	PUNCT
ap-7354	81	33	ync)2	ync)2	PROPN
ap-7354	81	34	)	)	PUNCT
ap-7354	81	35	1	1	NUM
ap-7354	81	36	2	2	NUM
ap-7354	81	37	.	.	PUNCT
ap-7354	82	1	(	(	PUNCT
ap-7354	82	2	5	5	X
ap-7354	82	3	)	)	PUNCT
ap-7354	82	4	these	these	DET
ap-7354	82	5	new	new	PROPN
ap-7354	82	6	hermitian	hermitian	ADJ
ap-7354	82	7	dnc	dnc	PROPN
ap-7354	82	8	variables	variable	NOUN
ap-7354	82	9	satisfy	satisfy	VERB
ap-7354	82	10	the	the	DET
ap-7354	82	11	following	follow	VERB
ap-7354	82	12	commutation	commutation	NOUN
ap-7354	82	13	relations	relation	NOUN
ap-7354	83	1	[	[	X
ap-7354	83	2	x	x	X
ap-7354	83	3	,	,	PUNCT
ap-7354	83	4	y	y	PROPN
ap-7354	83	5	]	]	X
ap-7354	83	6	=	=	PUNCT
ap-7354	83	7	iθ	iθ	NOUN
ap-7354	83	8	(	(	PUNCT
ap-7354	83	9	1	1	NUM
ap-7354	83	10	+	+	NUM
ap-7354	83	11	τy2	τy2	NOUN
ap-7354	83	12	)	)	PUNCT
ap-7354	83	13	,	,	PUNCT
ap-7354	84	1	[	[	X
ap-7354	84	2	y	y	NOUN
ap-7354	84	3	,	,	PUNCT
ap-7354	84	4	py	py	X
ap-7354	84	5	]	]	X
ap-7354	84	6	=	=	SYM
ap-7354	84	7	iℏ	iℏ	NOUN
ap-7354	84	8	(	(	PUNCT
ap-7354	84	9	1	1	NUM
ap-7354	84	10	+	+	NUM
ap-7354	84	11	τy2	τy2	NOUN
ap-7354	84	12	)	)	PUNCT
ap-7354	84	13	,	,	PUNCT
ap-7354	84	14	[	[	X
ap-7354	84	15	x	x	X
ap-7354	84	16	,	,	PUNCT
ap-7354	84	17	px	px	X
ap-7354	84	18	]	]	X
ap-7354	84	19	=	=	SYM
ap-7354	84	20	iℏ	iℏ	NOUN
ap-7354	84	21	(	(	PUNCT
ap-7354	84	22	1	1	NUM
ap-7354	84	23	+	+	NUM
ap-7354	84	24	τy2	τy2	NOUN
ap-7354	84	25	)	)	PUNCT
ap-7354	84	26	,	,	PUNCT
ap-7354	85	1	[	[	X
ap-7354	85	2	y	y	X
ap-7354	85	3	,	,	PUNCT
ap-7354	85	4	px	px	X
ap-7354	85	5	]	]	X
ap-7354	85	6	=	=	SYM
ap-7354	85	7	0	0	NUM
ap-7354	85	8	,	,	PUNCT
ap-7354	85	9	[	[	X
ap-7354	85	10	x	x	X
ap-7354	85	11	,	,	PUNCT
ap-7354	85	12	py	py	X
ap-7354	85	13	]	]	X
ap-7354	85	14	=	=	SYM
ap-7354	85	15	2iτy	2iτy	NUM
ap-7354	85	16	(	(	PUNCT
ap-7354	85	17	θpy	θpy	NOUN
ap-7354	85	18	+	+	CCONJ
ap-7354	85	19	ℏx	ℏx	X
ap-7354	85	20	)	)	PUNCT
ap-7354	85	21	,	,	PUNCT
ap-7354	86	1	[	[	X
ap-7354	86	2	px	px	X
ap-7354	86	3	,	,	PUNCT
ap-7354	86	4	py	py	X
ap-7354	86	5	]	]	X
ap-7354	86	6	=	=	SYM
ap-7354	86	7	0	0	X
ap-7354	86	8	.	.	PUNCT
ap-7354	87	1	(	(	PUNCT
ap-7354	87	2	6	6	NUM
ap-7354	87	3	)	)	PUNCT
ap-7354	87	4	now	now	ADV
ap-7354	87	5	,	,	PUNCT
ap-7354	87	6	using	use	VERB
ap-7354	87	7	bopp	bopp	VERB
ap-7354	87	8	-	-	PUNCT
ap-7354	87	9	shift	shift	NOUN
ap-7354	87	10	transformation	transformation	NOUN
ap-7354	87	11	[	[	X
ap-7354	87	12	31	31	NUM
ap-7354	87	13	]	]	PUNCT
ap-7354	87	14	,	,	PUNCT
ap-7354	87	15	one	one	PRON
ap-7354	87	16	can	can	AUX
ap-7354	87	17	express	express	VERB
ap-7354	87	18	the	the	DET
ap-7354	87	19	nc	nc	PROPN
ap-7354	87	20	variables	variable	NOUN
ap-7354	87	21	in	in	ADP
ap-7354	87	22	terms	term	NOUN
ap-7354	87	23	of	of	ADP
ap-7354	87	24	the	the	DET
ap-7354	87	25	standard	standard	ADJ
ap-7354	87	26	commutative	commutative	ADJ
ap-7354	87	27	variables	variable	NOUN
ap-7354	87	28	[	[	X
ap-7354	87	29	5	5	X
ap-7354	87	30	]	]	PUNCT
ap-7354	87	31	xnc	xnc	PROPN
ap-7354	87	32	=	=	SYM
ap-7354	87	33	xs	xs	PROPN
ap-7354	88	1	−	−	PROPN
ap-7354	88	2	θ	θ	PROPN
ap-7354	88	3	2ℏp	2ℏp	PROPN
ap-7354	88	4	s	s	PART
ap-7354	88	5	y	y	PROPN
ap-7354	88	6	,	,	PUNCT
ap-7354	88	7	pnc	pnc	NOUN
ap-7354	88	8	x	x	PUNCT
ap-7354	88	9	=	=	PUNCT
ap-7354	88	10	ps	ps	PROPN
ap-7354	88	11	x	x	PROPN
ap-7354	88	12	,	,	PUNCT
ap-7354	88	13	ync	ync	NOUN
ap-7354	88	14	=	=	NUM
ap-7354	88	15	ys	ys	PROPN
ap-7354	88	16	+	+	PROPN
ap-7354	88	17	θ	θ	PROPN
ap-7354	88	18	2ℏp	2ℏp	NOUN
ap-7354	88	19	s	s	PART
ap-7354	88	20	y	y	PROPN
ap-7354	88	21	,	,	PUNCT
ap-7354	88	22	pnc	pnc	PROPN
ap-7354	88	23	y	y	PROPN
ap-7354	88	24	=	=	PROPN
ap-7354	88	25	ps	ps	PROPN
ap-7354	88	26	y	y	PROPN
ap-7354	88	27	,	,	PUNCT
ap-7354	88	28	(	(	PUNCT
ap-7354	88	29	7	7	X
ap-7354	88	30	)	)	PUNCT
ap-7354	88	31	where	where	SCONJ
ap-7354	88	32	the	the	DET
ap-7354	88	33	index	index	NOUN
ap-7354	88	34	s	s	VERB
ap-7354	88	35	refers	refer	VERB
ap-7354	88	36	to	to	ADP
ap-7354	88	37	the	the	DET
ap-7354	88	38	standard	standard	ADJ
ap-7354	88	39	commutative	commutative	ADJ
ap-7354	88	40	space	space	NOUN
ap-7354	88	41	.	.	PUNCT
ap-7354	89	1	the	the	DET
ap-7354	89	2	interesting	interesting	ADJ
ap-7354	89	3	point	point	NOUN
ap-7354	89	4	is	be	AUX
ap-7354	89	5	that	that	SCONJ
ap-7354	89	6	in	in	ADP
ap-7354	89	7	the	the	DET
ap-7354	89	8	dnc	dnc	PROPN
ap-7354	89	9	space	space	NOUN
ap-7354	89	10	,	,	PUNCT
ap-7354	89	11	there	there	PRON
ap-7354	89	12	is	be	VERB
ap-7354	89	13	a	a	DET
ap-7354	89	14	minimum	minimum	ADJ
ap-7354	89	15	length	length	NOUN
ap-7354	89	16	for	for	ADP
ap-7354	89	17	x	x	PUNCT
ap-7354	89	18	in	in	ADP
ap-7354	89	19	a	a	DET
ap-7354	89	20	simultaneous	simultaneous	ADJ
ap-7354	89	21	x	x	NOUN
ap-7354	89	22	,	,	PUNCT
ap-7354	89	23	y	y	PROPN
ap-7354	89	24	measurement	measurement	NOUN
ap-7354	90	1	[	[	X
ap-7354	90	2	16	16	NUM
ap-7354	90	3	]	]	X
ap-7354	90	4	:	:	PUNCT
ap-7354	90	5	△	△	X
ap-7354	90	6	xmin	xmin	X
ap-7354	90	7	=	=	SYM
ap-7354	90	8	θ	θ	PROPN
ap-7354	90	9	√	√	NOUN
ap-7354	90	10	τ	τ	NUM
ap-7354	90	11	√	√	NOUN
ap-7354	90	12	1	1	NUM
ap-7354	90	13	+	+	NUM
ap-7354	90	14	τ	τ	X
ap-7354	90	15	⟨y	⟨y	X
ap-7354	90	16	⟩2	⟩2	PROPN
ap-7354	90	17	ρ	ρ	PROPN
ap-7354	90	18	,	,	PUNCT
ap-7354	90	19	(	(	PUNCT
ap-7354	90	20	8)	8)	NUM
ap-7354	90	21	as	as	ADV
ap-7354	90	22	well	well	ADV
ap-7354	90	23	,	,	PUNCT
ap-7354	90	24	in	in	ADP
ap-7354	90	25	a	a	DET
ap-7354	90	26	simultaneous	simultaneous	ADJ
ap-7354	90	27	y	y	NOUN
ap-7354	90	28	,	,	PUNCT
ap-7354	90	29	py	py	PROPN
ap-7354	90	30	measurement	measurement	NOUN
ap-7354	90	31	,	,	PUNCT
ap-7354	90	32	we	we	PRON
ap-7354	90	33	find	find	VERB
ap-7354	90	34	a	a	DET
ap-7354	90	35	minimal	minimal	ADJ
ap-7354	90	36	momentum	momentum	NOUN
ap-7354	90	37	as	as	ADP
ap-7354	90	38	△	△	X
ap-7354	90	39	(	(	PUNCT
ap-7354	90	40	py)min	py)min	X
ap-7354	90	41	=	=	SYM
ap-7354	90	42	ℏ	ℏ	PROPN
ap-7354	90	43	√	√	NOUN
ap-7354	90	44	τ	τ	PROPN
ap-7354	91	1	√	√	ADV
ap-7354	91	2	1	1	NUM
ap-7354	92	1	+	+	NUM
ap-7354	92	2	τ	τ	X
ap-7354	92	3	⟨y	⟨y	X
ap-7354	92	4	⟩2	⟩2	PROPN
ap-7354	92	5	ρ	ρ	PROPN
ap-7354	92	6	.	.	PUNCT
ap-7354	93	1	(	(	PUNCT
ap-7354	93	2	9	9	X
ap-7354	93	3	)	)	PUNCT
ap-7354	93	4	the	the	DET
ap-7354	93	5	motivation	motivation	NOUN
ap-7354	93	6	and	and	CCONJ
ap-7354	93	7	interesting	interesting	ADJ
ap-7354	93	8	physical	physical	ADJ
ap-7354	93	9	consequence	consequence	NOUN
ap-7354	93	10	for	for	ADP
ap-7354	93	11	position	position	NOUN
ap-7354	93	12	-	-	PUNCT
ap-7354	93	13	dependent	dependent	ADJ
ap-7354	93	14	noncommutativity	noncommutativity	NOUN
ap-7354	93	15	is	be	AUX
ap-7354	93	16	that	that	SCONJ
ap-7354	93	17	objects	object	NOUN
ap-7354	93	18	in	in	ADP
ap-7354	93	19	two	two	NUM
ap-7354	93	20	-	-	PUNCT
ap-7354	93	21	dimensional	dimensional	ADJ
ap-7354	93	22	spaces	space	NOUN
ap-7354	93	23	are	be	AUX
ap-7354	93	24	string	string	NOUN
ap-7354	93	25	-	-	PUNCT
ap-7354	93	26	like	like	ADJ
ap-7354	93	27	[	[	X
ap-7354	93	28	16	16	NUM
ap-7354	93	29	]	]	PUNCT
ap-7354	93	30	.	.	PUNCT
ap-7354	94	1	however	however	ADV
ap-7354	94	2	,	,	PUNCT
ap-7354	94	3	investigating	investigate	VERB
ap-7354	94	4	the	the	DET
ap-7354	94	5	do	do	NOUN
ap-7354	94	6	in	in	ADP
ap-7354	94	7	dnc	dnc	PROPN
ap-7354	94	8	geometry	geometry	NOUN
ap-7354	94	9	gives	give	VERB
ap-7354	94	10	rise	rise	NOUN
ap-7354	94	11	to	to	ADP
ap-7354	94	12	some	some	DET
ap-7354	94	13	phenomenological	phenomenological	ADJ
ap-7354	94	14	consequences	consequence	NOUN
ap-7354	94	15	that	that	PRON
ap-7354	94	16	may	may	AUX
ap-7354	94	17	be	be	AUX
ap-7354	94	18	very	very	ADV
ap-7354	94	19	important	important	ADJ
ap-7354	94	20	and	and	CCONJ
ap-7354	94	21	useful	useful	ADJ
ap-7354	94	22	.	.	PUNCT
ap-7354	95	1	3	3	X
ap-7354	95	2	.	.	X
ap-7354	95	3	two	two	NUM
ap-7354	95	4	-	-	PUNCT
ap-7354	95	5	dimensional	dimensional	ADJ
ap-7354	95	6	dirac	dirac	NOUN
ap-7354	95	7	oscillator	oscillator	NOUN
ap-7354	95	8	in	in	ADP
ap-7354	95	9	dynamical	dynamical	ADJ
ap-7354	95	10	noncommutative	noncommutative	ADJ
ap-7354	95	11	space	space	NOUN
ap-7354	95	12	3.1	3.1	NUM
ap-7354	95	13	.	.	PUNCT
ap-7354	95	14	extension	extension	NOUN
ap-7354	95	15	to	to	ADP
ap-7354	95	16	dynamical	dynamical	ADJ
ap-7354	95	17	noncommutative	noncommutative	ADJ
ap-7354	95	18	space	space	NOUN
ap-7354	95	19	the	the	DET
ap-7354	95	20	dynamics	dynamic	NOUN
ap-7354	95	21	of	of	ADP
ap-7354	95	22	the	the	DET
ap-7354	95	23	do	do	NOUN
ap-7354	95	24	in	in	ADP
ap-7354	95	25	the	the	DET
ap-7354	95	26	presence	presence	NOUN
ap-7354	95	27	of	of	ADP
ap-7354	95	28	a	a	DET
ap-7354	95	29	uniform	uniform	ADJ
ap-7354	95	30	external	external	ADJ
ap-7354	95	31	magnetic	magnetic	ADJ
ap-7354	95	32	field	field	NOUN
ap-7354	95	33	is	be	AUX
ap-7354	95	34	governed	govern	VERB
ap-7354	95	35	by	by	ADP
ap-7354	95	36	the	the	DET
ap-7354	95	37	following	follow	VERB
ap-7354	95	38	hamiltonian	hamiltonian	ADJ
ap-7354	95	39	hd	hd	PROPN
ap-7354	95	40	=	=	SYM
ap-7354	95	41	c−→α	c−→α	PROPN
ap-7354	95	42	.	.	PUNCT
ap-7354	96	1	(	(	PUNCT
ap-7354	96	2	−→p	−→p	NOUN
ap-7354	96	3	s	s	AUX
ap-7354	96	4	−	−	NOUN
ap-7354	96	5	e	e	NOUN
ap-7354	96	6	c	c	AUX
ap-7354	96	7	−→	−→	VERB
ap-7354	96	8	a	a	DET
ap-7354	96	9	s	s	NOUN
ap-7354	96	10	−	−	NOUN
ap-7354	96	11	imcωβ−→r	imcωβ−→r	X
ap-7354	96	12	s	s	PART
ap-7354	96	13	)	)	PUNCT
ap-7354	97	1	+	+	CCONJ
ap-7354	97	2	βmc2	βmc2	PROPN
ap-7354	97	3	,	,	PUNCT
ap-7354	97	4	(	(	PUNCT
ap-7354	97	5	10	10	NUM
ap-7354	97	6	)	)	PUNCT
ap-7354	97	7	where	where	SCONJ
ap-7354	97	8	−→	−→	NOUN
ap-7354	97	9	a	a	PRON
ap-7354	97	10	s	s	X
ap-7354	97	11	(	(	PUNCT
ap-7354	97	12	as	as	ADP
ap-7354	97	13	x	x	X
ap-7354	97	14	,	,	PUNCT
ap-7354	97	15	a	a	DET
ap-7354	97	16	s	s	PROPN
ap-7354	97	17	y	y	NOUN
ap-7354	97	18	,	,	PUNCT
ap-7354	97	19	a	a	DET
ap-7354	97	20	s	s	NOUN
ap-7354	97	21	z	z	NOUN
ap-7354	97	22	)	)	PUNCT
ap-7354	97	23	is	be	AUX
ap-7354	97	24	the	the	DET
ap-7354	97	25	vector	vector	NOUN
ap-7354	97	26	potential	potential	NOUN
ap-7354	97	27	produced	produce	VERB
ap-7354	97	28	by	by	ADP
ap-7354	97	29	the	the	DET
ap-7354	97	30	external	external	ADJ
ap-7354	97	31	magnetic	magnetic	ADJ
ap-7354	97	32	field	field	NOUN
ap-7354	97	33	and	and	CCONJ
ap-7354	97	34	e	e	NOUN
ap-7354	97	35	is	be	AUX
ap-7354	97	36	the	the	DET
ap-7354	97	37	charge	charge	NOUN
ap-7354	97	38	of	of	ADP
ap-7354	97	39	the	the	DET
ap-7354	97	40	do	do	NOUN
ap-7354	97	41	(	(	PUNCT
ap-7354	97	42	the	the	DET
ap-7354	97	43	electron	electron	NOUN
ap-7354	97	44	charge	charge	NOUN
ap-7354	97	45	)	)	PUNCT
ap-7354	97	46	.	.	PUNCT
ap-7354	98	1	the	the	DET
ap-7354	98	2	α⃗	α⃗	NOUN
ap-7354	98	3	matrices	matrix	NOUN
ap-7354	98	4	,	,	PUNCT
ap-7354	98	5	in	in	ADP
ap-7354	98	6	two	two	NUM
ap-7354	98	7	dimensions	dimension	NOUN
ap-7354	98	8	,	,	PUNCT
ap-7354	98	9	are	be	AUX
ap-7354	98	10	represented	represent	VERB
ap-7354	98	11	by	by	ADP
ap-7354	98	12	the	the	DET
ap-7354	98	13	following	follow	VERB
ap-7354	98	14	pauli	pauli	PROPN
ap-7354	98	15	matrices	matrice	VERB
ap-7354	99	1	α1	α1	PROPN
ap-7354	99	2	=	=	SYM
ap-7354	99	3	σx	σx	NOUN
ap-7354	99	4	=	=	PUNCT
ap-7354	99	5	(	(	PUNCT
ap-7354	99	6	0	0	NUM
ap-7354	99	7	1	1	NUM
ap-7354	99	8	1	1	NUM
ap-7354	99	9	0	0	NUM
ap-7354	99	10	)	)	PUNCT
ap-7354	99	11	,	,	PUNCT
ap-7354	99	12	α2	α2	NOUN
ap-7354	99	13	=	=	SYM
ap-7354	99	14	σy	σy	NOUN
ap-7354	99	15	=	=	PUNCT
ap-7354	99	16	(	(	PUNCT
ap-7354	99	17	0	0	NUM
ap-7354	99	18	−i	−i	NOUN
ap-7354	99	19	i	i	INTJ
ap-7354	99	20	0	0	NUM
ap-7354	99	21	)	)	PUNCT
ap-7354	99	22	,	,	PUNCT
ap-7354	99	23	β	β	X
ap-7354	99	24	=	=	PUNCT
ap-7354	99	25	σz	σz	NOUN
ap-7354	99	26	=	=	SYM
ap-7354	99	27	(	(	PUNCT
ap-7354	99	28	1	1	NUM
ap-7354	99	29	0	0	NUM
ap-7354	99	30	0	0	NUM
ap-7354	99	31	−1	−1	NOUN
ap-7354	99	32	)	)	PUNCT
ap-7354	99	33	,	,	PUNCT
ap-7354	99	34	(	(	PUNCT
ap-7354	99	35	11	11	NUM
ap-7354	99	36	)	)	PUNCT
ap-7354	99	37	which	which	PRON
ap-7354	99	38	satisfy	satisfy	VERB
ap-7354	99	39	the	the	DET
ap-7354	99	40	following	follow	VERB
ap-7354	99	41	relations	relation	NOUN
ap-7354	99	42	α2	α2	ADV
ap-7354	99	43	i	i	PRON
ap-7354	99	44	=	=	SYM
ap-7354	99	45	β2	β2	NOUN
ap-7354	99	46	=	=	NOUN
ap-7354	99	47	1	1	NUM
ap-7354	99	48	,	,	PUNCT
ap-7354	99	49	αiαj	αiαj	VERB
ap-7354	99	50	+	+	CCONJ
ap-7354	99	51	αjαi	αjαi	NOUN
ap-7354	99	52	=	=	SYM
ap-7354	99	53	0	0	NUM
ap-7354	99	54	,	,	PUNCT
ap-7354	99	55	αiβ	αiβ	NOUN
ap-7354	99	56	+	+	CCONJ
ap-7354	99	57	βαi	βαi	NOUN
ap-7354	99	58	=	=	SYM
ap-7354	99	59	0	0	X
ap-7354	99	60	.	.	PUNCT
ap-7354	100	1	i	i	PRON
ap-7354	100	2	=	=	NOUN
ap-7354	100	3	1	1	NUM
ap-7354	100	4	,	,	PUNCT
ap-7354	100	5	2	2	NUM
ap-7354	100	6	,	,	PUNCT
ap-7354	100	7	3	3	NUM
ap-7354	100	8	(	(	PUNCT
ap-7354	100	9	12	12	NUM
ap-7354	100	10	)	)	PUNCT
ap-7354	100	11	in	in	ADP
ap-7354	100	12	two	two	NUM
ap-7354	100	13	dimensions	dimension	NOUN
ap-7354	100	14	,	,	PUNCT
ap-7354	100	15	equation	equation	NOUN
ap-7354	100	16	(	(	PUNCT
ap-7354	100	17	10	10	NUM
ap-7354	100	18	)	)	PUNCT
ap-7354	100	19	becomes	become	VERB
ap-7354	100	20	691	691	NUM
ap-7354	100	21	ilyas	ilyas	PROPN
ap-7354	100	22	haouam	haouam	PROPN
ap-7354	100	23	acta	acta	PROPN
ap-7354	100	24	polytechnica	polytechnica	PROPN
ap-7354	100	25	hd	hd	PROPN
ap-7354	101	1	=	=	SYM
ap-7354	101	2	c	c	X
ap-7354	101	3	(	(	PUNCT
ap-7354	101	4	α1p	α1p	PROPN
ap-7354	101	5	s	s	NOUN
ap-7354	101	6	x	x	NOUN
ap-7354	101	7	+	+	NUM
ap-7354	101	8	α2p	α2p	NUM
ap-7354	101	9	s	s	PART
ap-7354	101	10	y	y	PROPN
ap-7354	101	11	)	)	PUNCT
ap-7354	101	12	−	−	PROPN
ap-7354	102	1	e	e	X
ap-7354	102	2	(	(	PUNCT
ap-7354	102	3	α1a	α1a	PRON
ap-7354	102	4	s	s	NOUN
ap-7354	102	5	x	x	X
ap-7354	102	6	+	+	NUM
ap-7354	102	7	α2a	α2a	PROPN
ap-7354	102	8	s	s	PART
ap-7354	102	9	y	y	PROPN
ap-7354	102	10	)	)	PUNCT
ap-7354	102	11	−	−	PROPN
ap-7354	103	1	imcω	imcω	ADJ
ap-7354	103	2	(	(	PUNCT
ap-7354	103	3	α1βx	α1βx	X
ap-7354	103	4	s	s	X
ap-7354	103	5	+	+	X
ap-7354	103	6	α2βy	α2βy	NUM
ap-7354	103	7	s	s	X
ap-7354	103	8	)	)	PUNCT
ap-7354	103	9	+	+	CCONJ
ap-7354	103	10	βmc2	βmc2	PROPN
ap-7354	103	11	.	.	PUNCT
ap-7354	104	1	(	(	PUNCT
ap-7354	104	2	13	13	NUM
ap-7354	104	3	)	)	PUNCT
ap-7354	104	4	let	let	VERB
ap-7354	104	5	us	we	PRON
ap-7354	104	6	consider	consider	VERB
ap-7354	104	7	−→	−→	NOUN
ap-7354	104	8	b	b	NOUN
ap-7354	104	9	to	to	PART
ap-7354	104	10	be	be	AUX
ap-7354	104	11	along	along	ADP
ap-7354	104	12	the	the	DET
ap-7354	104	13	z	z	NOUN
ap-7354	104	14	axis	axis	NOUN
ap-7354	104	15	,	,	PUNCT
ap-7354	104	16	thus	thus	ADV
ap-7354	104	17	the	the	DET
ap-7354	104	18	vector	vector	NOUN
ap-7354	104	19	potential	potential	ADJ
ap-7354	104	20	a⃗s	a⃗s	PROPN
ap-7354	104	21	is	be	AUX
ap-7354	104	22	given	give	VERB
ap-7354	104	23	in	in	ADP
ap-7354	104	24	the	the	DET
ap-7354	104	25	landau	landau	NOUN
ap-7354	104	26	gauge	gauge	NOUN
ap-7354	104	27	by	by	ADP
ap-7354	104	28	−→	−→	NOUN
ap-7354	104	29	a	a	DET
ap-7354	104	30	=	=	SYM
ap-7354	104	31	b	b	SYM
ap-7354	104	32	2	2	NUM
ap-7354	104	33	(	(	PUNCT
ap-7354	104	34	−ys	−ys	PROPN
ap-7354	104	35	,	,	PUNCT
ap-7354	104	36	xs	xs	PROPN
ap-7354	104	37	,	,	PUNCT
ap-7354	104	38	0	0	NUM
ap-7354	104	39	)	)	PUNCT
ap-7354	104	40	,	,	PUNCT
ap-7354	104	41	(	(	PUNCT
ap-7354	104	42	14	14	NUM
ap-7354	104	43	)	)	PUNCT
ap-7354	104	44	therefore	therefore	ADV
ap-7354	104	45	,	,	PUNCT
ap-7354	104	46	we	we	PRON
ap-7354	104	47	have	have	AUX
ap-7354	104	48	hd	hd	NOUN
ap-7354	104	49	(	(	PUNCT
ap-7354	104	50	xs	xs	NOUN
ap-7354	104	51	i	i	PRON
ap-7354	104	52	,	,	PUNCT
ap-7354	105	1	p	p	X
ap-7354	105	2	s	s	X
ap-7354	105	3	i	i	NOUN
ap-7354	105	4	)	)	PUNCT
ap-7354	106	1	=	=	PUNCT
ap-7354	106	2	c	c	X
ap-7354	106	3	(	(	PUNCT
ap-7354	106	4	α1p	α1p	NOUN
ap-7354	106	5	s	s	NOUN
ap-7354	106	6	x	x	NOUN
ap-7354	106	7	+	+	NUM
ap-7354	106	8	α2p	α2p	NUM
ap-7354	106	9	s	s	PART
ap-7354	106	10	y	y	PROPN
ap-7354	106	11	)	)	PUNCT
ap-7354	107	1	+	+	CCONJ
ap-7354	107	2	e	e	X
ap-7354	107	3	b	b	X
ap-7354	107	4	2	2	NUM
ap-7354	107	5	(	(	PUNCT
ap-7354	107	6	α1y	α1y	PROPN
ap-7354	107	7	s	s	PART
ap-7354	107	8	−	−	PROPN
ap-7354	107	9	α2x	α2x	NUM
ap-7354	107	10	s	s	NOUN
ap-7354	107	11	)	)	PUNCT
ap-7354	107	12	−	−	PROPN
ap-7354	107	13	imcω	imcω	INTJ
ap-7354	107	14	(	(	PUNCT
ap-7354	107	15	α1βx	α1βx	X
ap-7354	107	16	s	s	X
ap-7354	107	17	+	+	X
ap-7354	107	18	α2βy	α2βy	NUM
ap-7354	107	19	s	s	X
ap-7354	107	20	)	)	PUNCT
ap-7354	107	21	+	+	CCONJ
ap-7354	107	22	βmc2	βmc2	PROPN
ap-7354	107	23	.	.	PUNCT
ap-7354	108	1	(	(	PUNCT
ap-7354	108	2	15	15	NUM
ap-7354	108	3	)	)	PUNCT
ap-7354	108	4	the	the	DET
ap-7354	108	5	above	above	ADJ
ap-7354	108	6	hamiltonian	hamiltonian	NOUN
ap-7354	108	7	in	in	ADP
ap-7354	108	8	dnc	dnc	PROPN
ap-7354	108	9	space	space	NOUN
ap-7354	108	10	turns	turn	VERB
ap-7354	108	11	to	to	ADP
ap-7354	108	12	hd	hd	PROPN
ap-7354	108	13	(	(	PUNCT
ap-7354	108	14	xi	xi	PROPN
ap-7354	108	15	,	,	PUNCT
ap-7354	108	16	pi	pi	NOUN
ap-7354	108	17	)	)	PUNCT
ap-7354	109	1	=	=	SYM
ap-7354	109	2	c	c	X
ap-7354	109	3	(	(	PUNCT
ap-7354	109	4	α1px	α1px	X
ap-7354	109	5	+	+	X
ap-7354	109	6	α2py	α2py	NUM
ap-7354	109	7	)	)	PUNCT
ap-7354	110	1	+	+	CCONJ
ap-7354	110	2	e	e	X
ap-7354	110	3	b	b	X
ap-7354	110	4	2	2	NUM
ap-7354	110	5	(	(	PUNCT
ap-7354	110	6	α1y	α1y	PROPN
ap-7354	110	7	−	−	PROPN
ap-7354	110	8	α2x	α2x	NUM
ap-7354	110	9	)	)	PUNCT
ap-7354	110	10	−	−	PROPN
ap-7354	110	11	imcω	imcω	ADJ
ap-7354	110	12	(	(	PUNCT
ap-7354	110	13	α1βx+	α1βx+	NOUN
ap-7354	110	14	α2βy	α2βy	PUNCT
ap-7354	110	15	)	)	PUNCT
ap-7354	111	1	+	+	CCONJ
ap-7354	111	2	βmc2	βmc2	PROPN
ap-7354	111	3	.	.	PUNCT
ap-7354	112	1	(	(	PUNCT
ap-7354	112	2	16	16	NUM
ap-7354	112	3	)	)	PUNCT
ap-7354	112	4	now	now	ADV
ap-7354	112	5	,	,	PUNCT
ap-7354	112	6	using	use	VERB
ap-7354	112	7	equation	equation	NOUN
ap-7354	112	8	(	(	PUNCT
ap-7354	112	9	5	5	NUM
ap-7354	112	10	)	)	PUNCT
ap-7354	112	11	,	,	PUNCT
ap-7354	112	12	we	we	PRON
ap-7354	112	13	express	express	VERB
ap-7354	112	14	the	the	DET
ap-7354	112	15	hamiltonian	hamiltonian	NOUN
ap-7354	112	16	above	above	ADV
ap-7354	112	17	in	in	ADP
ap-7354	112	18	terms	term	NOUN
ap-7354	112	19	of	of	ADP
ap-7354	112	20	nc	nc	PROPN
ap-7354	112	21	variables	variables	PROPN
ap-7354	112	22	hd	hd	PROPN
ap-7354	112	23	(	(	PUNCT
ap-7354	112	24	xnc	xnc	PROPN
ap-7354	112	25	i	i	PROPN
ap-7354	112	26	,	,	PUNCT
ap-7354	112	27	pnc	pnc	PROPN
ap-7354	112	28	i	i	PROPN
ap-7354	112	29	)	)	PUNCT
ap-7354	113	1	=	=	PUNCT
ap-7354	113	2	βmc2	βmc2	PROPN
ap-7354	114	1	+	+	CCONJ
ap-7354	114	2	c[α1p	c[α1p	PROPN
ap-7354	114	3	nc	nc	PROPN
ap-7354	114	4	x	x	PROPN
ap-7354	114	5	+	+	CCONJ
ap-7354	114	6	α2	α2	ADJ
ap-7354	114	7	(	(	PUNCT
ap-7354	114	8	1	1	NUM
ap-7354	114	9	+	+	CCONJ
ap-7354	114	10	τ	τ	X
ap-7354	114	11	(	(	PUNCT
ap-7354	114	12	ync)2	ync)2	PROPN
ap-7354	114	13	)	)	PUNCT
ap-7354	114	14	1	1	NUM
ap-7354	114	15	2	2	NUM
ap-7354	114	16	pnc	pnc	NOUN
ap-7354	114	17	y	y	PROPN
ap-7354	114	18	(	(	PUNCT
ap-7354	114	19	1	1	NUM
ap-7354	114	20	+	+	CCONJ
ap-7354	114	21	τ	τ	X
ap-7354	114	22	(	(	PUNCT
ap-7354	114	23	ync)2	ync)2	PROPN
ap-7354	114	24	)	)	PUNCT
ap-7354	114	25	1	1	NUM
ap-7354	114	26	2	2	NUM
ap-7354	114	27	]	]	PUNCT
ap-7354	114	28	+	+	CCONJ
ap-7354	114	29	e	e	X
ap-7354	114	30	b	b	X
ap-7354	114	31	2	2	NUM
ap-7354	114	32	[	[	X
ap-7354	114	33	α1y	α1y	PROPN
ap-7354	114	34	nc	nc	PROPN
ap-7354	114	35	−	−	PROPN
ap-7354	114	36	α2	α2	PROPN
ap-7354	114	37	(	(	PUNCT
ap-7354	114	38	1	1	NUM
ap-7354	114	39	+	+	CCONJ
ap-7354	114	40	τ	τ	X
ap-7354	114	41	(	(	PUNCT
ap-7354	114	42	ync)2	ync)2	PROPN
ap-7354	114	43	)	)	PUNCT
ap-7354	114	44	1	1	NUM
ap-7354	114	45	2	2	NUM
ap-7354	114	46	xnc	xnc	PROPN
ap-7354	114	47	(	(	PUNCT
ap-7354	114	48	1	1	NUM
ap-7354	114	49	+	+	NUM
ap-7354	114	50	τ	τ	X
ap-7354	114	51	(	(	PUNCT
ap-7354	114	52	ync)2	ync)2	PROPN
ap-7354	114	53	)	)	PUNCT
ap-7354	114	54	1	1	NUM
ap-7354	114	55	2	2	NUM
ap-7354	114	56	]	]	PUNCT
ap-7354	114	57	−	−	PROPN
ap-7354	114	58	imcω[α1β	imcω[α1β	PROPN
ap-7354	114	59	(	(	PUNCT
ap-7354	114	60	1	1	NUM
ap-7354	114	61	+	+	NUM
ap-7354	114	62	τ	τ	X
ap-7354	114	63	(	(	PUNCT
ap-7354	114	64	ync)2	ync)2	PROPN
ap-7354	114	65	)	)	PUNCT
ap-7354	114	66	1	1	NUM
ap-7354	114	67	2	2	NUM
ap-7354	114	68	xnc	xnc	PROPN
ap-7354	114	69	(	(	PUNCT
ap-7354	114	70	1	1	NUM
ap-7354	114	71	+	+	NUM
ap-7354	114	72	τ	τ	X
ap-7354	114	73	(	(	PUNCT
ap-7354	114	74	ync)2	ync)2	PROPN
ap-7354	114	75	)	)	PUNCT
ap-7354	114	76	1	1	NUM
ap-7354	114	77	2	2	NUM
ap-7354	114	78	+	+	CCONJ
ap-7354	114	79	α2βy	α2βy	PUNCT
ap-7354	114	80	nc	nc	X
ap-7354	114	81	]	]	X
ap-7354	114	82	.	.	PUNCT
ap-7354	115	1	(	(	PUNCT
ap-7354	115	2	17	17	NUM
ap-7354	115	3	)	)	PUNCT
ap-7354	115	4	since	since	SCONJ
ap-7354	115	5	τ	τ	PROPN
ap-7354	115	6	is	be	AUX
ap-7354	115	7	very	very	ADV
ap-7354	115	8	small	small	ADJ
ap-7354	115	9	,	,	PUNCT
ap-7354	115	10	the	the	DET
ap-7354	115	11	parentheses	parenthesis	NOUN
ap-7354	115	12	can	can	AUX
ap-7354	115	13	be	be	AUX
ap-7354	115	14	expanded	expand	VERB
ap-7354	115	15	to	to	ADP
ap-7354	115	16	the	the	DET
ap-7354	115	17	first	first	ADJ
ap-7354	115	18	-	-	PUNCT
ap-7354	115	19	order	order	NOUN
ap-7354	115	20	through	through	ADP
ap-7354	115	21	(	(	PUNCT
ap-7354	115	22	1	1	NUM
ap-7354	115	23	+	+	NUM
ap-7354	115	24	τ	τ	X
ap-7354	115	25	(	(	PUNCT
ap-7354	115	26	ync)2	ync)2	PROPN
ap-7354	115	27	)	)	PUNCT
ap-7354	115	28	1	1	NUM
ap-7354	115	29	2	2	NUM
ap-7354	115	30	=	=	SYM
ap-7354	115	31	1	1	NUM
ap-7354	115	32	+	+	SYM
ap-7354	115	33	1	1	NUM
ap-7354	115	34	2τ	2τ	NUM
ap-7354	115	35	(	(	PUNCT
ap-7354	115	36	ync)2	ync)2	PROPN
ap-7354	115	37	,	,	PUNCT
ap-7354	115	38	(	(	PUNCT
ap-7354	115	39	18	18	NUM
ap-7354	115	40	)	)	PUNCT
ap-7354	115	41	so	so	SCONJ
ap-7354	115	42	that	that	SCONJ
ap-7354	115	43	equation	equation	NOUN
ap-7354	115	44	(	(	PUNCT
ap-7354	115	45	17	17	NUM
ap-7354	115	46	)	)	PUNCT
ap-7354	115	47	turns	turn	VERB
ap-7354	115	48	to	to	ADP
ap-7354	115	49	hd	hd	PROPN
ap-7354	115	50	(	(	PUNCT
ap-7354	115	51	xnc	xnc	PROPN
ap-7354	115	52	i	i	PROPN
ap-7354	115	53	,	,	PUNCT
ap-7354	115	54	pnc	pnc	PROPN
ap-7354	115	55	i	i	PROPN
ap-7354	115	56	)	)	PUNCT
ap-7354	116	1	=	=	PUNCT
ap-7354	116	2	c	c	X
ap-7354	116	3	[	[	PUNCT
ap-7354	116	4	α1p	α1p	X
ap-7354	116	5	nc	nc	X
ap-7354	116	6	x	x	PROPN
ap-7354	116	7	+	+	CCONJ
ap-7354	116	8	α2	α2	ADJ
ap-7354	116	9	{	{	PUNCT
ap-7354	116	10	pnc	pnc	PROPN
ap-7354	116	11	y	y	PROPN
ap-7354	116	12	+	+	PROPN
ap-7354	116	13	1	1	NUM
ap-7354	116	14	2τ	2τ	NUM
ap-7354	116	15	(	(	PUNCT
ap-7354	116	16	ync)2	ync)2	PROPN
ap-7354	116	17	pnc	pnc	PROPN
ap-7354	116	18	y	y	PROPN
ap-7354	116	19	+	+	PROPN
ap-7354	116	20	1	1	NUM
ap-7354	116	21	2τp	2τp	NOUN
ap-7354	116	22	nc	nc	PROPN
ap-7354	116	23	y	y	PROPN
ap-7354	116	24	(	(	PUNCT
ap-7354	116	25	ync)2	ync)2	PROPN
ap-7354	116	26	}	}	PUNCT
ap-7354	116	27	]	]	PUNCT
ap-7354	117	1	+	+	CCONJ
ap-7354	117	2	βmc2	βmc2	PROPN
ap-7354	117	3	+	+	CCONJ
ap-7354	117	4	e	e	X
ap-7354	117	5	b	b	X
ap-7354	117	6	2	2	NUM
ap-7354	117	7	[	[	PUNCT
ap-7354	117	8	α1y	α1y	PROPN
ap-7354	117	9	nc	nc	PROPN
ap-7354	117	10	−	−	PROPN
ap-7354	117	11	α2	α2	PROPN
ap-7354	117	12	{	{	PUNCT
ap-7354	117	13	xnc	xnc	PROPN
ap-7354	117	14	+	+	CCONJ
ap-7354	117	15	1	1	NUM
ap-7354	117	16	2τ	2τ	NUM
ap-7354	117	17	(	(	PUNCT
ap-7354	117	18	ync)2	ync)2	PROPN
ap-7354	117	19	xnc	xnc	PROPN
ap-7354	117	20	+	+	CCONJ
ap-7354	117	21	1	1	NUM
ap-7354	117	22	2τx	2τx	PROPN
ap-7354	117	23	nc	nc	PROPN
ap-7354	117	24	(	(	PUNCT
ap-7354	117	25	ync)2	ync)2	PROPN
ap-7354	117	26	}	}	PUNCT
ap-7354	117	27	]	]	PUNCT
ap-7354	117	28	−	−	PROPN
ap-7354	117	29	imcω	imcω	PROPN
ap-7354	117	30	[	[	PUNCT
ap-7354	117	31	α2βy	α2βy	X
ap-7354	117	32	nc	nc	X
ap-7354	117	33	+	+	CCONJ
ap-7354	117	34	α1β	α1β	PRON
ap-7354	117	35	{	{	PUNCT
ap-7354	117	36	xnc	xnc	PROPN
ap-7354	117	37	+	+	CCONJ
ap-7354	117	38	1	1	NUM
ap-7354	117	39	2τ	2τ	NUM
ap-7354	117	40	(	(	PUNCT
ap-7354	117	41	ync)2	ync)2	PROPN
ap-7354	117	42	xnc	xnc	PROPN
ap-7354	117	43	+	+	CCONJ
ap-7354	117	44	1	1	NUM
ap-7354	117	45	2τx	2τx	PROPN
ap-7354	117	46	nc	nc	PROPN
ap-7354	117	47	(	(	PUNCT
ap-7354	117	48	ync)2	ync)2	PROPN
ap-7354	117	49	}	}	PUNCT
ap-7354	117	50	]	]	PUNCT
ap-7354	117	51	.	.	PUNCT
ap-7354	118	1	(	(	PUNCT
ap-7354	118	2	19	19	NUM
ap-7354	118	3	)	)	PUNCT
ap-7354	118	4	using	use	VERB
ap-7354	118	5	the	the	DET
ap-7354	118	6	bopp	bopp	ADJ
ap-7354	118	7	-	-	PUNCT
ap-7354	118	8	shift	shift	NOUN
ap-7354	118	9	transformation	transformation	NOUN
ap-7354	118	10	(	(	PUNCT
ap-7354	118	11	7	7	NUM
ap-7354	118	12	)	)	PUNCT
ap-7354	118	13	,	,	PUNCT
ap-7354	118	14	hamiltonian	hamiltonian	NOUN
ap-7354	118	15	(	(	PUNCT
ap-7354	118	16	19	19	NUM
ap-7354	118	17	)	)	PUNCT
ap-7354	118	18	can	can	AUX
ap-7354	118	19	be	be	AUX
ap-7354	118	20	expressed	express	VERB
ap-7354	118	21	in	in	ADP
ap-7354	118	22	terms	term	NOUN
ap-7354	118	23	of	of	ADP
ap-7354	118	24	the	the	DET
ap-7354	118	25	standard	standard	ADJ
ap-7354	118	26	commutative	commutative	ADJ
ap-7354	118	27	variables	variable	NOUN
ap-7354	118	28	hd	hd	PROPN
ap-7354	118	29	(	(	PUNCT
ap-7354	118	30	xs	xs	NOUN
ap-7354	118	31	i	i	PRON
ap-7354	118	32	,	,	PUNCT
ap-7354	118	33	ps	ps	PROPN
ap-7354	118	34	i	i	INTJ
ap-7354	118	35	)	)	PUNCT
ap-7354	119	1	=	=	PUNCT
ap-7354	120	1	cα1ps	cα1ps	PROPN
ap-7354	120	2	x	x	SYM
ap-7354	120	3	+	+	CCONJ
ap-7354	120	4	βmc2	βmc2	PROPN
ap-7354	121	1	+	+	CCONJ
ap-7354	121	2	cα2ps	cα2ps	NOUN
ap-7354	121	3	y	y	NOUN
ap-7354	122	1	+	+	CCONJ
ap-7354	122	2	cα2	cα2	PROPN
ap-7354	122	3	{	{	PUNCT
ap-7354	122	4	1	1	NUM
ap-7354	122	5	2τ	2τ	NUM
ap-7354	122	6	(	(	PUNCT
ap-7354	122	7	ys	ys	NOUN
ap-7354	122	8	+	+	CCONJ
ap-7354	122	9	θ	θ	PROPN
ap-7354	122	10	2ℏps	2ℏps	NUM
ap-7354	122	11	x	x	X
ap-7354	122	12	)	)	PUNCT
ap-7354	122	13	2	2	NUM
ap-7354	122	14	ps	ps	NOUN
ap-7354	122	15	y	y	PROPN
ap-7354	122	16	+	+	NOUN
ap-7354	122	17	1	1	NUM
ap-7354	122	18	2τps	2τps	NUM
ap-7354	122	19	y	y	PROPN
ap-7354	122	20	(	(	PUNCT
ap-7354	122	21	ys	ys	PROPN
ap-7354	122	22	+	+	CCONJ
ap-7354	122	23	θ	θ	PROPN
ap-7354	122	24	2ℏps	2ℏps	NUM
ap-7354	122	25	x	x	X
ap-7354	122	26	)	)	PUNCT
ap-7354	122	27	2	2	NUM
ap-7354	122	28	}	}	PUNCT
ap-7354	123	1	+	+	CCONJ
ap-7354	123	2	eb	eb	PROPN
ap-7354	123	3	2	2	NUM
ap-7354	123	4	[	[	PUNCT
ap-7354	123	5	α1	α1	PROPN
ap-7354	123	6	(	(	PUNCT
ap-7354	123	7	ys	ys	NOUN
ap-7354	123	8	+	+	CCONJ
ap-7354	123	9	θ	θ	PROPN
ap-7354	123	10	2ℏps	2ℏps	NUM
ap-7354	123	11	x	x	X
ap-7354	123	12	)	)	PUNCT
ap-7354	123	13	−	−	PROPN
ap-7354	124	1	α2	α2	ADV
ap-7354	124	2	{	{	PUNCT
ap-7354	124	3	τ	τ	PROPN
ap-7354	124	4	2	2	NUM
ap-7354	124	5	(	(	PUNCT
ap-7354	124	6	ys	ys	NOUN
ap-7354	124	7	+	+	CCONJ
ap-7354	124	8	θ	θ	PROPN
ap-7354	124	9	2ℏps	2ℏps	NUM
ap-7354	124	10	x	x	X
ap-7354	124	11	)	)	PUNCT
ap-7354	124	12	2	2	NUM
ap-7354	124	13	(	(	PUNCT
ap-7354	124	14	xs	xs	NOUN
ap-7354	124	15	−	−	PROPN
ap-7354	125	1	θ	θ	PROPN
ap-7354	125	2	2ℏps	2ℏps	NUM
ap-7354	125	3	y	y	NOUN
ap-7354	125	4	)	)	PUNCT
ap-7354	126	1	+	+	NOUN
ap-7354	126	2	xs	xs	PROPN
ap-7354	126	3	−	−	NUM
ap-7354	126	4	θ	θ	PROPN
ap-7354	127	1	2ℏps	2ℏps	NUM
ap-7354	127	2	y	y	NOUN
ap-7354	127	3	+	+	CCONJ
ap-7354	127	4	1	1	NUM
ap-7354	127	5	2τ	2τ	NUM
ap-7354	127	6	(	(	PUNCT
ap-7354	127	7	xs	xs	PROPN
ap-7354	127	8	−	−	PROPN
ap-7354	127	9	θ	θ	PROPN
ap-7354	127	10	2ℏps	2ℏps	NUM
ap-7354	127	11	y	y	NOUN
ap-7354	127	12	)	)	PUNCT
ap-7354	127	13	(	(	PUNCT
ap-7354	127	14	ys	ys	NOUN
ap-7354	127	15	+	+	CCONJ
ap-7354	127	16	θ	θ	PROPN
ap-7354	127	17	2ℏps	2ℏps	NUM
ap-7354	127	18	x	x	X
ap-7354	127	19	)	)	PUNCT
ap-7354	127	20	2	2	NUM
ap-7354	127	21	}	}	PUNCT
ap-7354	127	22	]	]	PUNCT
ap-7354	128	1	−	−	PROPN
ap-7354	128	2	imcω	imcω	VERB
ap-7354	128	3	[	[	PUNCT
ap-7354	128	4	α2β	α2β	PROPN
ap-7354	128	5	(	(	PUNCT
ap-7354	128	6	ys	ys	NOUN
ap-7354	128	7	+	+	CCONJ
ap-7354	128	8	θ	θ	PROPN
ap-7354	128	9	2ℏps	2ℏps	NUM
ap-7354	128	10	x	x	X
ap-7354	128	11	)	)	PUNCT
ap-7354	129	1	+	+	CCONJ
ap-7354	129	2	α1β	α1β	PRON
ap-7354	129	3	{	{	PUNCT
ap-7354	129	4	xs	xs	NOUN
ap-7354	129	5	−	−	NUM
ap-7354	129	6	θ	θ	PROPN
ap-7354	129	7	2ℏps	2ℏps	NUM
ap-7354	129	8	y	y	PROPN
ap-7354	129	9	+	+	NOUN
ap-7354	129	10	τ	τ	X
ap-7354	129	11	2	2	NUM
ap-7354	129	12	(	(	PUNCT
ap-7354	129	13	ys	ys	NOUN
ap-7354	129	14	+	+	CCONJ
ap-7354	129	15	θ	θ	PROPN
ap-7354	129	16	2ℏps	2ℏps	NUM
ap-7354	129	17	x	x	X
ap-7354	129	18	)	)	PUNCT
ap-7354	129	19	2	2	NUM
ap-7354	129	20	(	(	PUNCT
ap-7354	129	21	xs	xs	NOUN
ap-7354	129	22	−	−	PROPN
ap-7354	129	23	θ	θ	PROPN
ap-7354	129	24	2ℏps	2ℏps	NUM
ap-7354	129	25	y	y	NOUN
ap-7354	129	26	)	)	PUNCT
ap-7354	129	27	+	+	CCONJ
ap-7354	129	28	τ	τ	X
ap-7354	129	29	2	2	NUM
ap-7354	129	30	(	(	PUNCT
ap-7354	129	31	xs	xs	PROPN
ap-7354	129	32	−	−	PROPN
ap-7354	129	33	θ	θ	PROPN
ap-7354	129	34	2ℏps	2ℏps	NUM
ap-7354	129	35	y	y	NOUN
ap-7354	129	36	)	)	PUNCT
ap-7354	129	37	(	(	PUNCT
ap-7354	129	38	ys	ys	NOUN
ap-7354	129	39	+	+	CCONJ
ap-7354	129	40	θ	θ	PROPN
ap-7354	129	41	2ℏps	2ℏps	NUM
ap-7354	129	42	x	x	X
ap-7354	129	43	)	)	PUNCT
ap-7354	129	44	2	2	NUM
ap-7354	129	45	}	}	PUNCT
ap-7354	129	46	]	]	PUNCT
ap-7354	129	47	.	.	PUNCT
ap-7354	130	1	(	(	PUNCT
ap-7354	130	2	20	20	NUM
ap-7354	130	3	)	)	PUNCT
ap-7354	130	4	therefore	therefore	ADV
ap-7354	130	5	,	,	PUNCT
ap-7354	130	6	to	to	ADP
ap-7354	130	7	the	the	DET
ap-7354	130	8	first	first	ADJ
ap-7354	130	9	-	-	PUNCT
ap-7354	130	10	order	order	NOUN
ap-7354	130	11	in	in	ADP
ap-7354	130	12	θ	θ	PROPN
ap-7354	130	13	and	and	CCONJ
ap-7354	130	14	τ	τ	PROPN
ap-7354	130	15	,	,	PUNCT
ap-7354	130	16	we	we	PRON
ap-7354	130	17	have	have	AUX
ap-7354	130	18	(	(	PUNCT
ap-7354	130	19	noting	note	VERB
ap-7354	130	20	that	that	SCONJ
ap-7354	130	21	terms	term	NOUN
ap-7354	130	22	containing	contain	VERB
ap-7354	130	23	θτ	θτ	NOUN
ap-7354	130	24	are	be	AUX
ap-7354	130	25	neglected	neglect	VERB
ap-7354	130	26	too	too	ADV
ap-7354	130	27	)	)	PUNCT
ap-7354	130	28	692	692	NUM
ap-7354	130	29	vol	vol	NOUN
ap-7354	130	30	.	.	PUNCT
ap-7354	131	1	61	61	NUM
ap-7354	131	2	no	no	NOUN
ap-7354	131	3	.	.	PUNCT
ap-7354	132	1	6/2021	6/2021	NUM
ap-7354	132	2	dirac	dirac	NOUN
ap-7354	132	3	oscillator	oscillator	NOUN
ap-7354	132	4	in	in	ADP
ap-7354	132	5	dynamical	dynamical	ADJ
ap-7354	132	6	noncommutative	noncommutative	ADJ
ap-7354	132	7	space	space	NOUN
ap-7354	132	8	hd	hd	PROPN
ap-7354	132	9	(	(	PUNCT
ap-7354	132	10	xs	xs	NOUN
ap-7354	132	11	i	i	INTJ
ap-7354	132	12	,	,	PUNCT
ap-7354	133	1	p	p	X
ap-7354	133	2	s	s	X
ap-7354	133	3	i	i	NOUN
ap-7354	133	4	)	)	PUNCT
ap-7354	134	1	=	=	PUNCT
ap-7354	134	2	c	c	X
ap-7354	134	3	[	[	PUNCT
ap-7354	134	4	α1p	α1p	NUM
ap-7354	134	5	s	s	X
ap-7354	134	6	x	x	X
ap-7354	134	7	+	+	X
ap-7354	134	8	α2	α2	ADJ
ap-7354	134	9	{	{	PUNCT
ap-7354	134	10	ps	ps	NOUN
ap-7354	134	11	y	y	PROPN
ap-7354	134	12	+	+	CCONJ
ap-7354	134	13	τ	τ	X
ap-7354	134	14	2	2	NUM
ap-7354	134	15	(	(	PUNCT
ap-7354	134	16	ys)2	ys)2	NOUN
ap-7354	134	17	ps	ps	PROPN
ap-7354	134	18	y	y	PROPN
ap-7354	134	19	+	+	PROPN
ap-7354	134	20	1	1	NUM
ap-7354	134	21	2τp	2τp	NOUN
ap-7354	134	22	s	s	PART
ap-7354	134	23	y	y	PROPN
ap-7354	134	24	(	(	PUNCT
ap-7354	134	25	ys)2	ys)2	PROPN
ap-7354	134	26	}	}	PUNCT
ap-7354	134	27	]	]	PUNCT
ap-7354	135	1	+	+	CCONJ
ap-7354	135	2	βmc2	βmc2	PROPN
ap-7354	135	3	+	+	CCONJ
ap-7354	135	4	e	e	PROPN
ap-7354	135	5	b	b	X
ap-7354	135	6	2	2	NUM
ap-7354	135	7	[	[	PUNCT
ap-7354	135	8	α1	α1	PROPN
ap-7354	135	9	(	(	PUNCT
ap-7354	135	10	ys	ys	NOUN
ap-7354	135	11	+	+	CCONJ
ap-7354	135	12	θ	θ	PROPN
ap-7354	135	13	2ℏp	2ℏp	NOUN
ap-7354	135	14	s	s	PART
ap-7354	135	15	x	x	X
ap-7354	135	16	)	)	PUNCT
ap-7354	135	17	−	−	PROPN
ap-7354	135	18	α2	α2	PROPN
ap-7354	135	19	{	{	PUNCT
ap-7354	135	20	xs	xs	PROPN
ap-7354	136	1	−	−	PROPN
ap-7354	136	2	θ	θ	PROPN
ap-7354	136	3	2ℏp	2ℏp	PROPN
ap-7354	136	4	s	s	PART
ap-7354	136	5	y	y	PROPN
ap-7354	136	6	+	+	CCONJ
ap-7354	136	7	τxs	τxs	PROPN
ap-7354	136	8	(	(	PUNCT
ap-7354	136	9	ys)2	ys)2	PROPN
ap-7354	136	10	}	}	PUNCT
ap-7354	136	11	]	]	PUNCT
ap-7354	137	1	−	−	PROPN
ap-7354	137	2	imcω	imcω	VERB
ap-7354	137	3	[	[	PUNCT
ap-7354	137	4	α2β	α2β	PROPN
ap-7354	137	5	(	(	PUNCT
ap-7354	137	6	ys	ys	NOUN
ap-7354	137	7	+	+	CCONJ
ap-7354	137	8	θ	θ	PROPN
ap-7354	137	9	2ℏp	2ℏp	NOUN
ap-7354	137	10	s	s	PART
ap-7354	137	11	x	x	PUNCT
ap-7354	137	12	)	)	PUNCT
ap-7354	138	1	+	+	CCONJ
ap-7354	138	2	α1β	α1β	PRON
ap-7354	138	3	{	{	PUNCT
ap-7354	138	4	xs	xs	NOUN
ap-7354	138	5	−	−	PROPN
ap-7354	138	6	θ	θ	PROPN
ap-7354	138	7	2ℏp	2ℏp	PROPN
ap-7354	138	8	s	s	PART
ap-7354	138	9	y	y	PROPN
ap-7354	138	10	+	+	CCONJ
ap-7354	138	11	τxs	τxs	PROPN
ap-7354	138	12	(	(	PUNCT
ap-7354	138	13	ys)2	ys)2	PROPN
ap-7354	138	14	}	}	PUNCT
ap-7354	138	15	]	]	PUNCT
ap-7354	138	16	,	,	PUNCT
ap-7354	138	17	(	(	PUNCT
ap-7354	138	18	21	21	NUM
ap-7354	138	19	)	)	PUNCT
ap-7354	138	20	which	which	PRON
ap-7354	138	21	can	can	AUX
ap-7354	138	22	be	be	AUX
ap-7354	138	23	written	write	VERB
ap-7354	138	24	as	as	ADP
ap-7354	138	25	hd	hd	NOUN
ap-7354	138	26	=	=	SYM
ap-7354	138	27	h0	h0	PROPN
ap-7354	138	28	+	+	NOUN
ap-7354	138	29	hθ	hθ	PROPN
ap-7354	138	30	+	+	NOUN
ap-7354	138	31	hτ	hτ	NOUN
ap-7354	138	32	,	,	PUNCT
ap-7354	138	33	(	(	PUNCT
ap-7354	138	34	22	22	NUM
ap-7354	138	35	)	)	PUNCT
ap-7354	138	36	with	with	ADP
ap-7354	138	37	h0	h0	PROPN
ap-7354	138	38	=	=	SYM
ap-7354	138	39	cα1p	cα1p	PROPN
ap-7354	138	40	s	s	PART
ap-7354	138	41	x	x	PROPN
ap-7354	138	42	+	+	CCONJ
ap-7354	138	43	cα2p	cα2p	PROPN
ap-7354	138	44	s	s	PROPN
ap-7354	138	45	y	y	PROPN
ap-7354	138	46	+	+	PROPN
ap-7354	138	47	eb	eb	PROPN
ap-7354	138	48	2	2	NUM
ap-7354	138	49	(	(	PUNCT
ap-7354	138	50	α1y	α1y	PROPN
ap-7354	138	51	s	s	PART
ap-7354	138	52	−	−	PROPN
ap-7354	138	53	α2x	α2x	NUM
ap-7354	138	54	s	s	NOUN
ap-7354	138	55	)	)	PUNCT
ap-7354	138	56	−	−	PROPN
ap-7354	138	57	imcω	imcω	INTJ
ap-7354	138	58	(	(	PUNCT
ap-7354	138	59	α1βx	α1βx	X
ap-7354	138	60	s	s	X
ap-7354	138	61	+	+	X
ap-7354	138	62	α2βy	α2βy	NUM
ap-7354	138	63	s	s	X
ap-7354	138	64	)	)	PUNCT
ap-7354	138	65	+	+	CCONJ
ap-7354	138	66	βmc2	βmc2	PROPN
ap-7354	138	67	,	,	PUNCT
ap-7354	138	68	(	(	PUNCT
ap-7354	138	69	23	23	NUM
ap-7354	138	70	)	)	PUNCT
ap-7354	138	71	hθ	hθ	NOUN
ap-7354	138	72	=	=	SYM
ap-7354	138	73	θ	θ	PROPN
ap-7354	138	74	2ℏ	2ℏ	NUM
ap-7354	138	75	[	[	PUNCT
ap-7354	138	76	eb	eb	PROPN
ap-7354	138	77	2	2	NUM
ap-7354	138	78	(	(	PUNCT
ap-7354	138	79	α1p	α1p	NUM
ap-7354	138	80	s	s	NOUN
ap-7354	138	81	x	x	NOUN
ap-7354	138	82	+	+	NUM
ap-7354	138	83	α2p	α2p	NUM
ap-7354	138	84	s	s	PART
ap-7354	138	85	y	y	PROPN
ap-7354	138	86	)	)	PUNCT
ap-7354	138	87	−	−	PROPN
ap-7354	139	1	imcω	imcω	VERB
ap-7354	139	2	(	(	PUNCT
ap-7354	139	3	α2βp	α2βp	NUM
ap-7354	139	4	s	s	NOUN
ap-7354	139	5	x	x	X
ap-7354	139	6	−	−	PROPN
ap-7354	139	7	α1βp	α1βp	PRON
ap-7354	139	8	s	s	NOUN
ap-7354	139	9	y	y	PROPN
ap-7354	139	10	)	)	PUNCT
ap-7354	139	11	]	]	PUNCT
ap-7354	139	12	,	,	PUNCT
ap-7354	139	13	(	(	PUNCT
ap-7354	139	14	24	24	NUM
ap-7354	139	15	)	)	PUNCT
ap-7354	139	16	hτ	hτ	NOUN
ap-7354	140	1	=	=	SYM
ap-7354	140	2	1	1	NUM
ap-7354	140	3	2τ	2τ	NUM
ap-7354	140	4	[	[	PUNCT
ap-7354	140	5	cα2	cα2	PROPN
ap-7354	140	6	(	(	PUNCT
ap-7354	140	7	ys)2	ys)2	NOUN
ap-7354	140	8	ps	ps	PROPN
ap-7354	140	9	y	y	PROPN
ap-7354	140	10	+	+	PROPN
ap-7354	140	11	cα2p	cα2p	PROPN
ap-7354	140	12	s	s	PROPN
ap-7354	140	13	y	y	PROPN
ap-7354	140	14	(	(	PUNCT
ap-7354	140	15	ys)2	ys)2	PROPN
ap-7354	140	16	−	−	PROPN
ap-7354	140	17	(	(	PUNCT
ap-7354	140	18	ebα2x	ebα2x	PROPN
ap-7354	140	19	s	s	PART
ap-7354	140	20	(	(	PUNCT
ap-7354	140	21	ys)2	ys)2	NOUN
ap-7354	140	22	−	−	PROPN
ap-7354	141	1	i2mcωα1βx	i2mcωα1βx	PROPN
ap-7354	141	2	s	s	X
ap-7354	141	3	(	(	PUNCT
ap-7354	141	4	ys)2	ys)2	PROPN
ap-7354	141	5	]	]	PUNCT
ap-7354	142	1	=	=	PUNCT
ap-7354	142	2	τ	τ	X
ap-7354	142	3	2	2	NUM
ap-7354	143	1	[	[	X
ap-7354	143	2	α2v1	α2v1	X
ap-7354	144	1	+	+	CCONJ
ap-7354	144	2	α2v2	α2v2	CCONJ
ap-7354	144	3	−	−	PROPN
ap-7354	145	1	(	(	PUNCT
ap-7354	145	2	ebα2	ebα2	PROPN
ap-7354	145	3	+	+	CCONJ
ap-7354	145	4	i2mcωα1β	i2mcωα1β	PROPN
ap-7354	145	5	)	)	PUNCT
ap-7354	145	6	v3	v3	PROPN
ap-7354	145	7	]	]	PUNCT
ap-7354	145	8	,	,	PUNCT
ap-7354	145	9	(	(	PUNCT
ap-7354	145	10	25	25	NUM
ap-7354	145	11	)	)	PUNCT
ap-7354	145	12	where	where	SCONJ
ap-7354	145	13	v1	v1	NOUN
ap-7354	145	14	=	=	SYM
ap-7354	145	15	(	(	PUNCT
ap-7354	145	16	ys)2	ys)2	PROPN
ap-7354	145	17	ps	ps	PROPN
ap-7354	145	18	y	y	PROPN
ap-7354	145	19	,	,	PUNCT
ap-7354	145	20	v2	v2	PROPN
ap-7354	145	21	=	=	SYM
ap-7354	145	22	ps	ps	NOUN
ap-7354	145	23	y	y	PROPN
ap-7354	145	24	(	(	PUNCT
ap-7354	145	25	ys)2	ys)2	PROPN
ap-7354	145	26	,	,	PUNCT
ap-7354	145	27	and	and	CCONJ
ap-7354	145	28	v3	v3	PROPN
ap-7354	145	29	=	=	SYM
ap-7354	145	30	xs	xs	PROPN
ap-7354	145	31	(	(	PUNCT
ap-7354	145	32	ys)2	ys)2	PROPN
ap-7354	145	33	.	.	PUNCT
ap-7354	146	1	(	(	PUNCT
ap-7354	146	2	26	26	NUM
ap-7354	146	3	)	)	PUNCT
ap-7354	146	4	knowing	know	VERB
ap-7354	146	5	that	that	SCONJ
ap-7354	146	6	hτ	hτ	PROPN
ap-7354	146	7	is	be	VERB
ap-7354	146	8	the	the	DET
ap-7354	146	9	perturbation	perturbation	NOUN
ap-7354	146	10	hamiltonian	hamiltonian	NOUN
ap-7354	146	11	in	in	ADP
ap-7354	146	12	which	which	PRON
ap-7354	146	13	it	it	PRON
ap-7354	146	14	reflects	reflect	VERB
ap-7354	146	15	the	the	DET
ap-7354	146	16	effects	effect	NOUN
ap-7354	146	17	of	of	ADP
ap-7354	146	18	dynamical	dynamical	ADJ
ap-7354	146	19	noncommutativity	noncommutativity	NOUN
ap-7354	146	20	of	of	ADP
ap-7354	146	21	space	space	NOUN
ap-7354	146	22	on	on	ADP
ap-7354	146	23	the	the	DET
ap-7354	146	24	do	do	NOUN
ap-7354	146	25	hamiltonian	hamiltonian	NOUN
ap-7354	146	26	.	.	PUNCT
ap-7354	147	1	we	we	PRON
ap-7354	147	2	can	can	AUX
ap-7354	147	3	also	also	ADV
ap-7354	147	4	treat	treat	VERB
ap-7354	147	5	the	the	DET
ap-7354	147	6	term	term	NOUN
ap-7354	147	7	proportional	proportional	ADJ
ap-7354	147	8	to	to	ADP
ap-7354	147	9	θ	θ	PROPN
ap-7354	147	10	,	,	PUNCT
ap-7354	147	11	given	give	VERB
ap-7354	147	12	in	in	ADP
ap-7354	147	13	equation	equation	NOUN
ap-7354	147	14	(	(	PUNCT
ap-7354	147	15	24	24	NUM
ap-7354	147	16	)	)	PUNCT
ap-7354	147	17	as	as	ADP
ap-7354	147	18	a	a	DET
ap-7354	147	19	perturbation	perturbation	NOUN
ap-7354	147	20	term	term	NOUN
ap-7354	147	21	.	.	PUNCT
ap-7354	148	1	but	but	CCONJ
ap-7354	148	2	here	here	ADV
ap-7354	148	3	,	,	PUNCT
ap-7354	148	4	and	and	CCONJ
ap-7354	148	5	in	in	ADP
ap-7354	148	6	a	a	DET
ap-7354	148	7	different	different	ADJ
ap-7354	148	8	way	way	NOUN
ap-7354	148	9	,	,	PUNCT
ap-7354	148	10	we	we	PRON
ap-7354	148	11	will	will	AUX
ap-7354	148	12	accurately	accurately	ADV
ap-7354	148	13	calculate	calculate	VERB
ap-7354	148	14	the	the	DET
ap-7354	148	15	energy	energy	NOUN
ap-7354	148	16	of	of	ADP
ap-7354	148	17	the	the	DET
ap-7354	148	18	deformed	deform	VERB
ap-7354	148	19	system	system	NOUN
ap-7354	148	20	h0	h0	NOUN
ap-7354	148	21	+	+	PROPN
ap-7354	148	22	hθ	hθ	PROPN
ap-7354	148	23	and	and	CCONJ
ap-7354	148	24	employ	employ	VERB
ap-7354	148	25	it	it	PRON
ap-7354	148	26	to	to	PART
ap-7354	148	27	test	test	VERB
ap-7354	148	28	the	the	DET
ap-7354	148	29	effect	effect	NOUN
ap-7354	148	30	of	of	ADP
ap-7354	148	31	the	the	DET
ap-7354	148	32	dnc	dnc	PROPN
ap-7354	148	33	space	space	NOUN
ap-7354	148	34	on	on	ADP
ap-7354	148	35	the	the	DET
ap-7354	148	36	do	do	NOUN
ap-7354	148	37	.	.	PUNCT
ap-7354	149	1	thus	thus	ADV
ap-7354	149	2	,	,	PUNCT
ap-7354	149	3	we	we	PRON
ap-7354	149	4	consider	consider	VERB
ap-7354	149	5	the	the	DET
ap-7354	149	6	following	following	ADJ
ap-7354	149	7	unperturbed	unperturbed	ADJ
ap-7354	149	8	system	system	NOUN
ap-7354	149	9	hunp	hunp	NOUN
ap-7354	149	10	=	=	SYM
ap-7354	149	11	h0	h0	PROPN
ap-7354	149	12	+	+	NOUN
ap-7354	149	13	hθ	hθ	PROPN
ap-7354	149	14	.	.	PUNCT
ap-7354	150	1	(	(	PUNCT
ap-7354	150	2	27	27	NUM
ap-7354	150	3	)	)	PUNCT
ap-7354	150	4	while	while	SCONJ
ap-7354	150	5	the	the	DET
ap-7354	150	6	noncommutativity	noncommutativity	NOUN
ap-7354	150	7	parameter	parameter	PROPN
ap-7354	150	8	τ	τ	PROPN
ap-7354	150	9	is	be	AUX
ap-7354	150	10	non	non	ADJ
ap-7354	150	11	-	-	ADJ
ap-7354	150	12	zero	zero	NUM
ap-7354	150	13	and	and	CCONJ
ap-7354	150	14	very	very	ADV
ap-7354	150	15	small	small	ADJ
ap-7354	150	16	,	,	PUNCT
ap-7354	150	17	one	one	PRON
ap-7354	150	18	can	can	AUX
ap-7354	150	19	use	use	VERB
ap-7354	150	20	the	the	DET
ap-7354	150	21	perturbation	perturbation	NOUN
ap-7354	150	22	theory	theory	NOUN
ap-7354	150	23	to	to	PART
ap-7354	150	24	find	find	VERB
ap-7354	150	25	the	the	DET
ap-7354	150	26	spectrum	spectrum	NOUN
ap-7354	150	27	of	of	ADP
ap-7354	150	28	the	the	DET
ap-7354	150	29	systems	system	NOUN
ap-7354	150	30	in	in	ADP
ap-7354	150	31	question	question	NOUN
ap-7354	150	32	.	.	PUNCT
ap-7354	151	1	the	the	DET
ap-7354	151	2	two	two	NUM
ap-7354	151	3	-	-	PUNCT
ap-7354	151	4	dimensional	dimensional	ADJ
ap-7354	151	5	do	do	NOUN
ap-7354	151	6	equation	equation	NOUN
ap-7354	151	7	in	in	ADP
ap-7354	151	8	the	the	DET
ap-7354	151	9	dnc	dnc	PROPN
ap-7354	151	10	space	space	NOUN
ap-7354	151	11	is	be	AUX
ap-7354	151	12	written	write	VERB
ap-7354	151	13	as	as	SCONJ
ap-7354	151	14	follows	follow	VERB
ap-7354	151	15	hd	hd	NOUN
ap-7354	151	16	|ψd⟩	|ψd⟩	NOUN
ap-7354	151	17	=	=	SYM
ap-7354	151	18	(	(	PUNCT
ap-7354	151	19	hunp	hunp	PROPN
ap-7354	151	20	+	+	PROPN
ap-7354	151	21	hτ	hτ	NOUN
ap-7354	151	22	)	)	PUNCT
ap-7354	151	23	|ψd⟩	|ψd⟩	VERB
ap-7354	151	24	=	=	SYM
ap-7354	151	25	eθ	eθ	PROPN
ap-7354	151	26	,	,	PUNCT
ap-7354	151	27	τ	τ	X
ap-7354	151	28	|ψd⟩	|ψd⟩	INTJ
ap-7354	151	29	,	,	PUNCT
ap-7354	151	30	(	(	PUNCT
ap-7354	151	31	28	28	NUM
ap-7354	151	32	)	)	PUNCT
ap-7354	151	33	with	with	ADP
ap-7354	151	34	|ψd⟩	|ψd⟩	NOUN
ap-7354	151	35	=	=	SYM
ap-7354	151	36	(	(	PUNCT
ap-7354	151	37	|ψ1⟩	|ψ1⟩	PROPN
ap-7354	151	38	,	,	PUNCT
ap-7354	151	39	|ψ2⟩)t	|ψ2⟩)t	PROPN
ap-7354	151	40	,	,	PUNCT
ap-7354	151	41	(	(	PUNCT
ap-7354	151	42	29	29	NUM
ap-7354	151	43	)	)	PUNCT
ap-7354	151	44	being	be	AUX
ap-7354	151	45	the	the	DET
ap-7354	151	46	wave	wave	NOUN
ap-7354	151	47	function	function	NOUN
ap-7354	151	48	of	of	ADP
ap-7354	151	49	the	the	DET
ap-7354	151	50	system	system	NOUN
ap-7354	151	51	in	in	ADP
ap-7354	151	52	question	question	NOUN
ap-7354	151	53	.	.	PUNCT
ap-7354	152	1	693	693	NUM
ap-7354	152	2	ilyas	ilyas	PROPN
ap-7354	152	3	haouam	haouam	PROPN
ap-7354	152	4	acta	acta	PROPN
ap-7354	152	5	polytechnica	polytechnica	PROPN
ap-7354	152	6	3.2	3.2	NUM
ap-7354	152	7	.	.	PUNCT
ap-7354	153	1	unperturbed	unperturbed	ADJ
ap-7354	153	2	eigenvalues	eigenvalue	NOUN
ap-7354	153	3	and	and	CCONJ
ap-7354	153	4	eigenvectors	eigenvector	NOUN
ap-7354	153	5	we	we	PRON
ap-7354	153	6	introduce	introduce	VERB
ap-7354	153	7	the	the	DET
ap-7354	153	8	following	follow	VERB
ap-7354	153	9	complex	complex	ADJ
ap-7354	153	10	coordinates	coordinate	NOUN
ap-7354	153	11	zs	zs	X
ap-7354	153	12	=	=	SYM
ap-7354	153	13	xs	xs	PROPN
ap-7354	153	14	+	+	CCONJ
ap-7354	153	15	iys	iys	PROPN
ap-7354	153	16	,	,	PUNCT
ap-7354	153	17	zs	zs	PROPN
ap-7354	153	18	=	=	SYM
ap-7354	153	19	xs	xs	PROPN
ap-7354	153	20	−	−	PROPN
ap-7354	153	21	iys	iys	PROPN
ap-7354	153	22	,	,	PUNCT
ap-7354	153	23	(	(	PUNCT
ap-7354	153	24	30	30	NUM
ap-7354	153	25	)	)	PUNCT
ap-7354	153	26	ps	ps	NOUN
ap-7354	153	27	z	z	NOUN
ap-7354	153	28	=	=	SYM
ap-7354	153	29	−iℏ	−iℏ	PROPN
ap-7354	154	1	d	d	NOUN
ap-7354	154	2	dzs	dzs	NOUN
ap-7354	154	3	=	=	NOUN
ap-7354	154	4	1	1	NUM
ap-7354	154	5	2	2	NUM
ap-7354	154	6	(	(	PUNCT
ap-7354	154	7	ps	ps	NOUN
ap-7354	154	8	x	x	SYM
ap-7354	154	9	−	−	PROPN
ap-7354	154	10	ips	ips	X
ap-7354	154	11	y	y	PROPN
ap-7354	154	12	)	)	PUNCT
ap-7354	154	13	,	,	PUNCT
ap-7354	154	14	ps	ps	PROPN
ap-7354	154	15	z	z	NOUN
ap-7354	154	16	=	=	SYM
ap-7354	154	17	−iℏ	−iℏ	PROPN
ap-7354	154	18	d	d	NOUN
ap-7354	154	19	dzs	dzs	NOUN
ap-7354	154	20	=	=	NOUN
ap-7354	154	21	1	1	NUM
ap-7354	154	22	2	2	NUM
ap-7354	154	23	(	(	PUNCT
ap-7354	154	24	ps	ps	NOUN
ap-7354	154	25	x	x	PROPN
ap-7354	154	26	+	+	CCONJ
ap-7354	154	27	ips	ips	PROPN
ap-7354	154	28	y	y	PROPN
ap-7354	154	29	)	)	PUNCT
ap-7354	154	30	,	,	PUNCT
ap-7354	154	31	(	(	PUNCT
ap-7354	154	32	31	31	NUM
ap-7354	154	33	)	)	PUNCT
ap-7354	154	34	where	where	SCONJ
ap-7354	154	35	[	[	X
ap-7354	154	36	zs	zs	X
ap-7354	154	37	,	,	PUNCT
ap-7354	154	38	ps	ps	PROPN
ap-7354	154	39	z	z	X
ap-7354	154	40	]	]	X
ap-7354	155	1	=	=	PUNCT
ap-7354	156	1	[	[	X
ap-7354	156	2	z̄s	z̄s	NOUN
ap-7354	156	3	,	,	PUNCT
ap-7354	156	4	ps	ps	PROPN
ap-7354	156	5	z	z	X
ap-7354	156	6	]	]	X
ap-7354	156	7	=	=	PUNCT
ap-7354	156	8	iℏ	iℏ	NOUN
ap-7354	156	9	,	,	PUNCT
ap-7354	156	10	[	[	X
ap-7354	156	11	zs	zs	X
ap-7354	156	12	,	,	PUNCT
ap-7354	156	13	ps	ps	PROPN
ap-7354	156	14	z	z	X
ap-7354	156	15	]	]	X
ap-7354	156	16	=	=	PUNCT
ap-7354	157	1	[	[	X
ap-7354	157	2	z̄s	z̄s	NOUN
ap-7354	157	3	,	,	PUNCT
ap-7354	157	4	ps	ps	PROPN
ap-7354	157	5	z	z	X
ap-7354	157	6	]	]	X
ap-7354	157	7	=	=	SYM
ap-7354	157	8	0	0	X
ap-7354	157	9	.	.	PUNCT
ap-7354	157	10	(	(	PUNCT
ap-7354	157	11	32	32	NUM
ap-7354	157	12	)	)	PUNCT
ap-7354	157	13	using	use	VERB
ap-7354	157	14	equation	equation	NOUN
ap-7354	157	15	(	(	PUNCT
ap-7354	157	16	11	11	NUM
ap-7354	157	17	)	)	PUNCT
ap-7354	157	18	,	,	PUNCT
ap-7354	157	19	our	our	PRON
ap-7354	157	20	unperturbed	unperturbed	ADJ
ap-7354	157	21	system	system	NOUN
ap-7354	157	22	(	(	PUNCT
ap-7354	157	23	24	24	NUM
ap-7354	157	24	)	)	PUNCT
ap-7354	157	25	,	,	PUNCT
ap-7354	157	26	in	in	ADP
ap-7354	157	27	the	the	DET
ap-7354	157	28	complex	complex	ADJ
ap-7354	157	29	formalism	formalism	NOUN
ap-7354	157	30	,	,	PUNCT
ap-7354	157	31	merely	merely	ADV
ap-7354	157	32	becomes	become	VERB
ap-7354	157	33	hunp	hunp	NOUN
ap-7354	157	34	=	=	PUNCT
ap-7354	158	1	[	[	PUNCT
ap-7354	158	2	mc2	mc2	PROPN
ap-7354	158	3	2cωps	2cωps	NUM
ap-7354	158	4	z	z	NOUN
ap-7354	158	5	+	+	NUM
ap-7354	158	6	imczsω̃	imczsω̃	NUM
ap-7354	158	7	2cωps	2cωps	NUM
ap-7354	158	8	z	z	NOUN
ap-7354	158	9	−	−	PROPN
ap-7354	158	10	imcωzsω̃	imcωzsω̃	NOUN
ap-7354	158	11	−mc2	−mc2	NOUN
ap-7354	158	12	]	]	PUNCT
ap-7354	158	13	,	,	PUNCT
ap-7354	158	14	(	(	PUNCT
ap-7354	158	15	33	33	NUM
ap-7354	158	16	)	)	PUNCT
ap-7354	158	17	where	where	SCONJ
ap-7354	158	18	ω	ω	NOUN
ap-7354	158	19	=	=	SYM
ap-7354	158	20	1	1	NUM
ap-7354	159	1	+	+	NOUN
ap-7354	159	2	m	m	VERB
ap-7354	159	3	θω̃	θω̃	VERB
ap-7354	159	4	2ℏ	2ℏ	NUM
ap-7354	159	5	with	with	ADP
ap-7354	159	6	ω̃	ω̃	PROPN
ap-7354	159	7	=	=	SYM
ap-7354	159	8	ω	ω	NUM
ap-7354	159	9	−	−	NOUN
ap-7354	159	10	ωc	ωc	SYM
ap-7354	159	11	2	2	NUM
ap-7354	159	12	,	,	PUNCT
ap-7354	159	13	(	(	PUNCT
ap-7354	159	14	34	34	NUM
ap-7354	159	15	)	)	PUNCT
ap-7354	159	16	knowing	know	VERB
ap-7354	159	17	that	that	SCONJ
ap-7354	159	18	ωc	ωc	PROPN
ap-7354	159	19	=	=	SYM
ap-7354	159	20	|e|b	|e|b	PROPN
ap-7354	159	21	mc	mc	PROPN
ap-7354	159	22	is	be	AUX
ap-7354	159	23	the	the	DET
ap-7354	159	24	cyclotron	cyclotron	NOUN
ap-7354	159	25	frequency	frequency	NOUN
ap-7354	159	26	.	.	PUNCT
ap-7354	160	1	now	now	ADV
ap-7354	160	2	,	,	PUNCT
ap-7354	160	3	let	let	VERB
ap-7354	160	4	us	we	PRON
ap-7354	160	5	introduce	introduce	VERB
ap-7354	160	6	the	the	DET
ap-7354	160	7	following	follow	VERB
ap-7354	160	8	creation	creation	NOUN
ap-7354	160	9	and	and	CCONJ
ap-7354	160	10	annihilation	annihilation	NOUN
ap-7354	160	11	operators	operator	NOUN
ap-7354	160	12	a	a	DET
ap-7354	160	13	=	=	X
ap-7354	160	14	i	i	PRON
ap-7354	160	15	(	(	PUNCT
ap-7354	160	16	ω√	ω√	X
ap-7354	160	17	mωℏ	mωℏ	NOUN
ap-7354	160	18	ps	ps	NOUN
ap-7354	160	19	z	z	PROPN
ap-7354	160	20	−	−	PROPN
ap-7354	161	1	i	i	PRON
ap-7354	161	2	2ω	2ω	VERB
ap-7354	162	1	√	√	NUM
ap-7354	162	2	mω	mω	PROPN
ap-7354	162	3	ℏ	ℏ	PROPN
ap-7354	162	4	zs	zs	PROPN
ap-7354	162	5	)	)	PUNCT
ap-7354	162	6	,	,	PUNCT
ap-7354	162	7	(	(	PUNCT
ap-7354	162	8	35	35	NUM
ap-7354	162	9	)	)	PUNCT
ap-7354	162	10	a†	a†	NOUN
ap-7354	162	11	=	=	SYM
ap-7354	162	12	−i	−i	PROPN
ap-7354	162	13	(	(	PUNCT
ap-7354	162	14	ω√	ω√	X
ap-7354	162	15	mωℏ	mωℏ	NOUN
ap-7354	162	16	ps	ps	NOUN
ap-7354	162	17	z	z	PROPN
ap-7354	163	1	+	+	NUM
ap-7354	163	2	i	i	PRON
ap-7354	163	3	2ω	2ω	NUM
ap-7354	163	4	√	√	NUM
ap-7354	163	5	mω	mω	PROPN
ap-7354	163	6	ℏ	ℏ	PROPN
ap-7354	163	7	zs	zs	PROPN
ap-7354	163	8	)	)	PUNCT
ap-7354	163	9	,	,	PUNCT
ap-7354	163	10	(	(	PUNCT
ap-7354	163	11	36	36	NUM
ap-7354	163	12	)	)	PUNCT
ap-7354	163	13	that	that	PRON
ap-7354	163	14	satisfy	satisfy	VERB
ap-7354	163	15	the	the	DET
ap-7354	163	16	following	follow	VERB
ap-7354	163	17	commutations	commutation	NOUN
ap-7354	163	18	relations	relation	NOUN
ap-7354	163	19	[	[	PUNCT
ap-7354	163	20	a	a	X
ap-7354	163	21	,	,	PUNCT
ap-7354	163	22	a†	a†	NOUN
ap-7354	163	23	]	]	X
ap-7354	163	24	=	=	SYM
ap-7354	163	25	1	1	NUM
ap-7354	163	26	,	,	PUNCT
ap-7354	163	27	[	[	X
ap-7354	163	28	a	a	X
ap-7354	163	29	,	,	PUNCT
ap-7354	163	30	a	a	X
ap-7354	163	31	]	]	X
ap-7354	163	32	=	=	SYM
ap-7354	163	33	[	[	PUNCT
ap-7354	163	34	a†	a†	X
ap-7354	163	35	,	,	PUNCT
ap-7354	163	36	a†	a†	X
ap-7354	163	37	]	]	PUNCT
ap-7354	163	38	=	=	SYM
ap-7354	163	39	0	0	X
ap-7354	163	40	.	.	PUNCT
ap-7354	164	1	(	(	PUNCT
ap-7354	164	2	37	37	NUM
ap-7354	164	3	)	)	PUNCT
ap-7354	164	4	thus	thus	ADV
ap-7354	164	5	,	,	PUNCT
ap-7354	164	6	in	in	ADP
ap-7354	164	7	terms	term	NOUN
ap-7354	164	8	of	of	ADP
ap-7354	164	9	the	the	DET
ap-7354	164	10	creation	creation	NOUN
ap-7354	164	11	and	and	CCONJ
ap-7354	164	12	annihilation	annihilation	NOUN
ap-7354	164	13	operators	operator	NOUN
ap-7354	164	14	,	,	PUNCT
ap-7354	164	15	the	the	DET
ap-7354	164	16	hamiltonian	hamiltonian	NOUN
ap-7354	164	17	(	(	PUNCT
ap-7354	164	18	33	33	NUM
ap-7354	164	19	)	)	PUNCT
ap-7354	164	20	takes	take	VERB
ap-7354	164	21	the	the	DET
ap-7354	164	22	following	follow	VERB
ap-7354	164	23	form	form	NOUN
ap-7354	164	24	hθ	hθ	NOUN
ap-7354	165	1	=	=	SYM
ap-7354	165	2	[	[	PUNCT
ap-7354	165	3	mc2	mc2	NOUN
ap-7354	165	4	i2c	i2c	NOUN
ap-7354	165	5	√	√	NUM
ap-7354	165	6	mωℏa†	mωℏa†	NOUN
ap-7354	165	7	−i2c	−i2c	NOUN
ap-7354	165	8	√	√	X
ap-7354	165	9	mωℏa	mωℏa	NOUN
ap-7354	165	10	−mc2	−mc2	NOUN
ap-7354	165	11	]	]	PUNCT
ap-7354	165	12	=	=	PUNCT
ap-7354	166	1	[	[	PUNCT
ap-7354	166	2	mc2	mc2	PROPN
ap-7354	166	3	iga†	iga†	PROPN
ap-7354	166	4	−iga	−iga	NOUN
ap-7354	166	5	−mc2	−mc2	NOUN
ap-7354	166	6	]	]	PUNCT
ap-7354	166	7	,	,	PUNCT
ap-7354	166	8	(	(	PUNCT
ap-7354	166	9	38	38	NUM
ap-7354	166	10	)	)	PUNCT
ap-7354	166	11	with	with	ADP
ap-7354	166	12	g	g	PROPN
ap-7354	166	13	=	=	SYM
ap-7354	166	14	2c	2c	NUM
ap-7354	166	15	√	√	NOUN
ap-7354	166	16	mℏω	mℏω	NOUN
ap-7354	166	17	being	be	AUX
ap-7354	166	18	a	a	DET
ap-7354	166	19	parameter	parameter	NOUN
ap-7354	166	20	that	that	PRON
ap-7354	166	21	describes	describe	VERB
ap-7354	166	22	the	the	DET
ap-7354	166	23	coupling	coupling	NOUN
ap-7354	166	24	between	between	ADP
ap-7354	166	25	different	different	ADJ
ap-7354	166	26	states	state	NOUN
ap-7354	166	27	in	in	ADP
ap-7354	166	28	nc	nc	PROPN
ap-7354	166	29	space	space	NOUN
ap-7354	166	30	,	,	PUNCT
ap-7354	166	31	and	and	CCONJ
ap-7354	166	32	ω	ω	NUM
ap-7354	166	33	=	=	SYM
ap-7354	166	34	ωω̃	ωω̃	PUNCT
ap-7354	166	35	being	be	AUX
ap-7354	166	36	the	the	DET
ap-7354	166	37	correction	correction	NOUN
ap-7354	166	38	of	of	ADP
ap-7354	166	39	the	the	DET
ap-7354	166	40	frequency	frequency	NOUN
ap-7354	166	41	ω̃	ω̃	PROPN
ap-7354	166	42	of	of	ADP
ap-7354	166	43	the	the	DET
ap-7354	166	44	commutative	commutative	ADJ
ap-7354	166	45	space	space	NOUN
ap-7354	166	46	.	.	PUNCT
ap-7354	167	1	in	in	ADP
ap-7354	167	2	addition	addition	NOUN
ap-7354	167	3	,	,	PUNCT
ap-7354	167	4	the	the	DET
ap-7354	167	5	parameter	parameter	NOUN
ap-7354	167	6	g	g	PROPN
ap-7354	167	7	=	=	PROPN
ap-7354	167	8	2c	2c	NUM
ap-7354	167	9	√	√	PROPN
ap-7354	167	10	mω̃ℏ	mω̃ℏ	PROPN
ap-7354	167	11	describes	describe	VERB
ap-7354	167	12	the	the	DET
ap-7354	167	13	coupling	coupling	NOUN
ap-7354	167	14	between	between	ADP
ap-7354	167	15	different	different	ADJ
ap-7354	167	16	states	state	NOUN
ap-7354	167	17	in	in	ADP
ap-7354	167	18	the	the	DET
ap-7354	167	19	commutative	commutative	ADJ
ap-7354	167	20	space	space	NOUN
ap-7354	167	21	.	.	PUNCT
ap-7354	168	1	now	now	ADV
ap-7354	168	2	,	,	PUNCT
ap-7354	168	3	we	we	PRON
ap-7354	168	4	solve	solve	VERB
ap-7354	168	5	the	the	DET
ap-7354	168	6	following	follow	VERB
ap-7354	168	7	equation	equation	NOUN
ap-7354	168	8	hunp	hunp	NOUN
ap-7354	168	9	∣∣ψd	∣∣ψd	NOUN
ap-7354	168	10	〉	〉	NOUN
ap-7354	168	11	=	=	SYM
ap-7354	168	12	eθ	eθ	ADP
ap-7354	168	13	∣∣ψd	∣∣ψd	NOUN
ap-7354	168	14	〉	〉	NOUN
ap-7354	168	15	,	,	PUNCT
ap-7354	168	16	(	(	PUNCT
ap-7354	168	17	39	39	NUM
ap-7354	168	18	)	)	PUNCT
ap-7354	168	19	where	where	SCONJ
ap-7354	168	20	eθ	eθ	NOUN
ap-7354	168	21	,	,	PUNCT
ap-7354	168	22	∣∣ψd	∣∣ψd	NOUN
ap-7354	168	23	〉	〉	NOUN
ap-7354	168	24	are	be	AUX
ap-7354	168	25	the	the	DET
ap-7354	168	26	eigenenergy	eigenenergy	NOUN
ap-7354	168	27	and	and	CCONJ
ap-7354	168	28	wave	wave	NOUN
ap-7354	168	29	function	function	NOUN
ap-7354	168	30	of	of	ADP
ap-7354	168	31	the	the	DET
ap-7354	168	32	dirac	dirac	NOUN
ap-7354	168	33	equation	equation	NOUN
ap-7354	168	34	above	above	ADV
ap-7354	168	35	,	,	PUNCT
ap-7354	168	36	respectively	respectively	ADV
ap-7354	168	37	.	.	PUNCT
ap-7354	169	1	by	by	ADP
ap-7354	169	2	inserting	insert	VERB
ap-7354	169	3	equation	equation	NOUN
ap-7354	169	4	(	(	PUNCT
ap-7354	169	5	29	29	NUM
ap-7354	169	6	)	)	PUNCT
ap-7354	169	7	in	in	ADP
ap-7354	169	8	(	(	PUNCT
ap-7354	169	9	39	39	NUM
ap-7354	169	10	)	)	PUNCT
ap-7354	169	11	,	,	PUNCT
ap-7354	169	12	we	we	PRON
ap-7354	169	13	obtain	obtain	VERB
ap-7354	169	14	the	the	DET
ap-7354	169	15	following	follow	VERB
ap-7354	169	16	system	system	NOUN
ap-7354	169	17	of	of	ADP
ap-7354	169	18	equations	equation	NOUN
ap-7354	169	19	(	(	PUNCT
ap-7354	169	20	mc2	mc2	PROPN
ap-7354	169	21	iga†	iga†	PROPN
ap-7354	169	22	−iga	−iga	NOUN
ap-7354	169	23	−mc2	−mc2	NOUN
ap-7354	169	24	)	)	PUNCT
ap-7354	169	25	(	(	PUNCT
ap-7354	169	26	|	|	ADV
ap-7354	169	27	ψ1	ψ1	VERB
ap-7354	169	28	>	>	X
ap-7354	169	29	|	|	ADP
ap-7354	169	30	ψ2	ψ2	NOUN
ap-7354	169	31	>	>	X
ap-7354	169	32	)	)	PUNCT
ap-7354	170	1	=	=	SYM
ap-7354	170	2	eθ	eθ	PROPN
ap-7354	170	3	(	(	PUNCT
ap-7354	170	4	|	|	ADV
ap-7354	170	5	ψ1	ψ1	VERB
ap-7354	170	6	>	>	X
ap-7354	170	7	|	|	ADP
ap-7354	170	8	ψ2	ψ2	NOUN
ap-7354	170	9	>	>	X
ap-7354	170	10	)	)	PUNCT
ap-7354	170	11	,	,	PUNCT
ap-7354	170	12	(	(	PUNCT
ap-7354	170	13	40	40	NUM
ap-7354	170	14	)	)	PUNCT
ap-7354	170	15	694	694	NUM
ap-7354	170	16	vol	vol	NOUN
ap-7354	170	17	.	.	PUNCT
ap-7354	171	1	61	61	NUM
ap-7354	171	2	no	no	NOUN
ap-7354	171	3	.	.	PUNCT
ap-7354	172	1	6/2021	6/2021	NUM
ap-7354	172	2	dirac	dirac	NOUN
ap-7354	172	3	oscillator	oscillator	NOUN
ap-7354	172	4	in	in	ADP
ap-7354	172	5	dynamical	dynamical	ADJ
ap-7354	172	6	noncommutative	noncommutative	ADJ
ap-7354	172	7	space	space	NOUN
ap-7354	172	8	where	where	SCONJ
ap-7354	172	9	(	(	PUNCT
ap-7354	172	10	mc2	mc2	PROPN
ap-7354	172	11	−	−	PROPN
ap-7354	172	12	eθ	eθ	PROPN
ap-7354	172	13	)	)	PUNCT
ap-7354	172	14	|	|	ADV
ap-7354	172	15	ψ1	ψ1	VERB
ap-7354	172	16	>	>	X
ap-7354	173	1	+	+	ADJ
ap-7354	173	2	iga†	iga†	ADJ
ap-7354	173	3	|	|	ADJ
ap-7354	173	4	ψ2	ψ2	VERB
ap-7354	173	5	>	>	PUNCT
ap-7354	173	6	=	=	SYM
ap-7354	173	7	0	0	NUM
ap-7354	173	8	,	,	PUNCT
ap-7354	173	9	(	(	PUNCT
ap-7354	173	10	41	41	NUM
ap-7354	173	11	)	)	PUNCT
ap-7354	173	12	−iga	−iga	ADV
ap-7354	173	13	|	|	ADV
ap-7354	173	14	ψ1	ψ1	VERB
ap-7354	173	15	>	>	X
ap-7354	173	16	−	−	PROPN
ap-7354	174	1	(	(	PUNCT
ap-7354	174	2	mc2	mc2	PROPN
ap-7354	174	3	+	+	CCONJ
ap-7354	174	4	eθ	eθ	NOUN
ap-7354	174	5	)	)	PUNCT
ap-7354	174	6	|	|	ADV
ap-7354	174	7	ψ2	ψ2	NOUN
ap-7354	174	8	>	>	PUNCT
ap-7354	174	9	=	=	SYM
ap-7354	174	10	0	0	NUM
ap-7354	174	11	.	.	PUNCT
ap-7354	175	1	(	(	PUNCT
ap-7354	175	2	42	42	NUM
ap-7354	175	3	)	)	PUNCT
ap-7354	175	4	from	from	ADP
ap-7354	175	5	the	the	DET
ap-7354	175	6	equations	equation	NOUN
ap-7354	175	7	(	(	PUNCT
ap-7354	175	8	41	41	NUM
ap-7354	175	9	)	)	PUNCT
ap-7354	175	10	and	and	CCONJ
ap-7354	175	11	(	(	PUNCT
ap-7354	175	12	42	42	NUM
ap-7354	175	13	)	)	PUNCT
ap-7354	175	14	,	,	PUNCT
ap-7354	175	15	we	we	PRON
ap-7354	175	16	have	have	VERB
ap-7354	175	17	|	|	ADV
ap-7354	175	18	ψ2	ψ2	NOUN
ap-7354	175	19	>	>	PUNCT
ap-7354	175	20	=	=	SYM
ap-7354	175	21	−iga	−iga	NOUN
ap-7354	175	22	eθ	eθ	PROPN
ap-7354	175	23	+	+	PROPN
ap-7354	175	24	mc2	mc2	PROPN
ap-7354	175	25	|	|	ADV
ap-7354	175	26	ψ1	ψ1	NOUN
ap-7354	175	27	>	>	X
ap-7354	175	28	,	,	PUNCT
ap-7354	175	29	(	(	PUNCT
ap-7354	175	30	43	43	NUM
ap-7354	175	31	)	)	PUNCT
ap-7354	175	32	subsequently	subsequently	ADV
ap-7354	175	33	[	[	PUNCT
ap-7354	175	34	g2a†a+m2c4	g2a†a+m2c4	NOUN
ap-7354	175	35	−	−	PROPN
ap-7354	175	36	(	(	PUNCT
ap-7354	175	37	eθ)2	eθ)2	PROPN
ap-7354	175	38	]	]	PUNCT
ap-7354	175	39	|	|	ADV
ap-7354	175	40	ψ1	ψ1	VERB
ap-7354	175	41	>	>	PUNCT
ap-7354	175	42	=	=	PROPN
ap-7354	176	1	0	0	PROPN
ap-7354	176	2	.	.	PUNCT
ap-7354	177	1	(	(	PUNCT
ap-7354	177	2	44	44	NUM
ap-7354	177	3	)	)	PUNCT
ap-7354	177	4	on	on	ADP
ap-7354	177	5	the	the	DET
ap-7354	177	6	basis	basis	NOUN
ap-7354	177	7	of	of	ADP
ap-7354	177	8	the	the	DET
ap-7354	177	9	second	second	ADJ
ap-7354	177	10	quantization	quantization	NOUN
ap-7354	177	11	,	,	PUNCT
ap-7354	177	12	of	of	ADP
ap-7354	177	13	which	which	PRON
ap-7354	177	14	|	|	ADV
ap-7354	177	15	ψ1	ψ1	VERB
ap-7354	177	16	>	>	PUNCT
ap-7354	177	17	≡|	≡|	NOUN
ap-7354	177	18	n	n	PRON
ap-7354	177	19	>	>	PUNCT
ap-7354	177	20	,	,	PUNCT
ap-7354	177	21	we	we	PRON
ap-7354	177	22	have	have	VERB
ap-7354	177	23	[	[	PUNCT
ap-7354	177	24	g2n+m2c4	g2n+m2c4	NOUN
ap-7354	177	25	−	−	PROPN
ap-7354	177	26	(	(	PUNCT
ap-7354	177	27	eθ)2	eθ)2	PROPN
ap-7354	177	28	]	]	PUNCT
ap-7354	177	29	|	|	ADV
ap-7354	177	30	n	n	X
ap-7354	177	31	>	>	PUNCT
ap-7354	177	32	=	=	SYM
ap-7354	177	33	0	0	NUM
ap-7354	177	34	,	,	PUNCT
ap-7354	177	35	a†a	a†a	PUNCT
ap-7354	177	36	|	|	NOUN
ap-7354	177	37	n	n	X
ap-7354	177	38	>	>	PUNCT
ap-7354	177	39	=	=	PUNCT
ap-7354	177	40	n	n	CCONJ
ap-7354	178	1	|	|	ADV
ap-7354	178	2	n	n	ADV
ap-7354	178	3	>	>	X
ap-7354	178	4	.	.	PUNCT
ap-7354	179	1	(	(	PUNCT
ap-7354	179	2	45	45	NUM
ap-7354	179	3	)	)	PUNCT
ap-7354	179	4	thus	thus	ADV
ap-7354	179	5	,	,	PUNCT
ap-7354	179	6	the	the	DET
ap-7354	179	7	energy	energy	NOUN
ap-7354	179	8	spectrum	spectrum	NOUN
ap-7354	179	9	is	be	AUX
ap-7354	179	10	given	give	VERB
ap-7354	179	11	by	by	ADP
ap-7354	179	12	e±	e±	PROPN
ap-7354	179	13	θ	θ	PROPN
ap-7354	179	14	,	,	PUNCT
ap-7354	179	15	n	n	NOUN
ap-7354	179	16	=	=	SYM
ap-7354	179	17	±	±	NOUN
ap-7354	179	18	√	√	PROPN
ap-7354	179	19	m2c4	m2c4	PROPN
ap-7354	179	20	+	+	CCONJ
ap-7354	179	21	g2n	g2n	ADJ
ap-7354	179	22	,	,	PUNCT
ap-7354	179	23	(	(	PUNCT
ap-7354	179	24	46	46	NUM
ap-7354	179	25	)	)	PUNCT
ap-7354	179	26	which	which	PRON
ap-7354	179	27	can	can	AUX
ap-7354	179	28	be	be	AUX
ap-7354	179	29	rewritten	rewrite	VERB
ap-7354	179	30	as	as	ADP
ap-7354	179	31	e±	e±	PROPN
ap-7354	179	32	θ	θ	PROPN
ap-7354	179	33	,	,	PUNCT
ap-7354	179	34	n	n	NOUN
ap-7354	179	35	=	=	NOUN
ap-7354	179	36	±mc2	±mc2	NOUN
ap-7354	179	37	√	√	NUM
ap-7354	179	38	1	1	NUM
ap-7354	179	39	+	+	CCONJ
ap-7354	179	40	4ℏω̃	4ℏω̃	NUM
ap-7354	179	41	mc2	mc2	NOUN
ap-7354	179	42	(	(	PUNCT
ap-7354	179	43	1	1	NUM
ap-7354	179	44	+	+	NOUN
ap-7354	179	45	m	m	PRON
ap-7354	179	46	θω̃	θω̃	ADJ
ap-7354	179	47	2ℏ	2ℏ	NUM
ap-7354	179	48	)	)	PUNCT
ap-7354	179	49	n	n	CCONJ
ap-7354	179	50	,	,	PUNCT
ap-7354	179	51	n	n	NOUN
ap-7354	179	52	=	=	SYM
ap-7354	179	53	0	0	NUM
ap-7354	179	54	,	,	PUNCT
ap-7354	179	55	1	1	NUM
ap-7354	179	56	,	,	PUNCT
ap-7354	179	57	2	2	NUM
ap-7354	179	58	,	,	PUNCT
ap-7354	179	59	...	...	PUNCT
ap-7354	179	60	(	(	PUNCT
ap-7354	179	61	47	47	NUM
ap-7354	179	62	)	)	PUNCT
ap-7354	179	63	furthermore	furthermore	ADV
ap-7354	179	64	,	,	PUNCT
ap-7354	179	65	we	we	PRON
ap-7354	179	66	have	have	VERB
ap-7354	179	67	the	the	DET
ap-7354	179	68	reduced	reduce	VERB
ap-7354	179	69	energy	energy	NOUN
ap-7354	179	70	spectrum	spectrum	NOUN
ap-7354	179	71	e±	e±	PROPN
ap-7354	179	72	n	n	CCONJ
ap-7354	179	73	e0	e0	PROPN
ap-7354	179	74	=	=	SYM
ap-7354	179	75	±	±	NOUN
ap-7354	179	76	√	√	NOUN
ap-7354	179	77	1	1	NUM
ap-7354	180	1	+	+	NUM
ap-7354	180	2	4w	4w	NOUN
ap-7354	180	3	(	(	PUNCT
ap-7354	180	4	1	1	NUM
ap-7354	180	5	+	+	SYM
ap-7354	180	6	1	1	NUM
ap-7354	180	7	2qw	2qw	ADJ
ap-7354	180	8	)	)	PUNCT
ap-7354	180	9	n	n	CCONJ
ap-7354	180	10	,	,	PUNCT
ap-7354	180	11	(	(	PUNCT
ap-7354	180	12	48	48	NUM
ap-7354	180	13	)	)	PUNCT
ap-7354	180	14	where	where	SCONJ
ap-7354	180	15	the	the	DET
ap-7354	180	16	non	non	ADJ
ap-7354	180	17	-	-	ADJ
ap-7354	180	18	relativistic	relativistic	ADJ
ap-7354	180	19	limit	limit	NOUN
ap-7354	180	20	feature	feature	NOUN
ap-7354	180	21	is	be	AUX
ap-7354	180	22	reduced	reduce	VERB
ap-7354	180	23	in	in	ADP
ap-7354	180	24	w	w	PROPN
ap-7354	180	25	=	=	PUNCT
ap-7354	180	26	ℏω̃	ℏω̃	NOUN
ap-7354	180	27	mc2	mc2	PROPN
ap-7354	180	28	,	,	PUNCT
ap-7354	180	29	which	which	PRON
ap-7354	180	30	is	be	AUX
ap-7354	180	31	a	a	DET
ap-7354	180	32	parameter	parameter	NOUN
ap-7354	180	33	that	that	PRON
ap-7354	180	34	controls	control	VERB
ap-7354	180	35	the	the	DET
ap-7354	180	36	nonrelativistic	nonrelativistic	ADJ
ap-7354	180	37	limit	limit	NOUN
ap-7354	180	38	within	within	ADP
ap-7354	180	39	the	the	DET
ap-7354	180	40	nc	nc	PROPN
ap-7354	180	41	space	space	NOUN
ap-7354	180	42	(	(	PUNCT
ap-7354	180	43	as	as	ADV
ap-7354	180	44	well	well	ADV
ap-7354	180	45	as	as	ADP
ap-7354	180	46	in	in	ADP
ap-7354	180	47	commutative	commutative	ADJ
ap-7354	180	48	case	case	NOUN
ap-7354	180	49	,	,	PUNCT
ap-7354	180	50	if	if	SCONJ
ap-7354	180	51	θ	θ	PROPN
ap-7354	180	52	=	=	SYM
ap-7354	180	53	0	0	NUM
ap-7354	180	54	)	)	PUNCT
ap-7354	180	55	,	,	PUNCT
ap-7354	180	56	and	and	CCONJ
ap-7354	180	57	e0	e0	PROPN
ap-7354	180	58	=	=	SYM
ap-7354	180	59	mc2	mc2	PROPN
ap-7354	180	60	is	be	AUX
ap-7354	180	61	a	a	DET
ap-7354	180	62	background	background	NOUN
ap-7354	180	63	energy	energy	NOUN
ap-7354	180	64	,	,	PUNCT
ap-7354	180	65	which	which	PRON
ap-7354	180	66	corresponds	correspond	VERB
ap-7354	180	67	to	to	ADP
ap-7354	180	68	n	n	NOUN
ap-7354	180	69	=	=	SYM
ap-7354	180	70	0	0	PROPN
ap-7354	180	71	.	.	PUNCT
ap-7354	181	1	and	and	CCONJ
ap-7354	181	2	q	q	NOUN
ap-7354	181	3	=	=	SYM
ap-7354	181	4	θ	θ	X
ap-7354	181	5	θ0	θ0	PROPN
ap-7354	181	6	with	with	ADP
ap-7354	181	7	θ0	θ0	PROPN
ap-7354	181	8	=	=	SYM
ap-7354	181	9	(	(	PUNCT
ap-7354	181	10	ℏ	ℏ	PROPN
ap-7354	181	11	mc	mc	NOUN
ap-7354	181	12	)	)	PUNCT
ap-7354	181	13	2of	2of	NOUN
ap-7354	181	14	the	the	DET
ap-7354	181	15	dimension	dimension	NOUN
ap-7354	181	16	[	[	PUNCT
ap-7354	181	17	ℏ	ℏ	X
ap-7354	181	18	mc	mc	X
ap-7354	181	19	]	]	SYM
ap-7354	181	20	2	2	NUM
ap-7354	181	21	=	=	SYM
ap-7354	181	22	l2	l2	NOUN
ap-7354	181	23	≡	≡	PROPN
ap-7354	181	24	m2	m2	PROPN
ap-7354	181	25	.	.	PUNCT
ap-7354	182	1	the	the	DET
ap-7354	182	2	corresponding	corresponding	ADJ
ap-7354	182	3	wave	wave	NOUN
ap-7354	182	4	function	function	NOUN
ap-7354	182	5	is	be	AUX
ap-7354	182	6	written	write	VERB
ap-7354	182	7	as	as	ADP
ap-7354	182	8	a	a	DET
ap-7354	182	9	function	function	NOUN
ap-7354	182	10	of	of	ADP
ap-7354	182	11	the	the	DET
ap-7354	182	12	basis	basis	NOUN
ap-7354	182	13	|	|	ADV
ap-7354	182	14	n	n	CCONJ
ap-7354	182	15	>	>	PUNCT
ap-7354	182	16	=	=	SYM
ap-7354	182	17	(	(	PUNCT
ap-7354	182	18	a†)n	a†)n	NOUN
ap-7354	182	19	√	√	PROPN
ap-7354	182	20	n	n	CCONJ
ap-7354	182	21	!	!	PUNCT
ap-7354	183	1	|	|	ADV
ap-7354	183	2	0	0	NUM
ap-7354	183	3	>	>	PUNCT
ap-7354	183	4	,	,	PUNCT
ap-7354	183	5	and	and	CCONJ
ap-7354	183	6	it	it	PRON
ap-7354	183	7	is	be	AUX
ap-7354	183	8	given	give	VERB
ap-7354	183	9	by	by	ADP
ap-7354	183	10	the	the	DET
ap-7354	183	11	following	follow	VERB
ap-7354	183	12	formula	formula	NOUN
ap-7354	184	1	|	|	ADV
ap-7354	184	2	ψ±	ψ±	NOUN
ap-7354	184	3	n	n	X
ap-7354	184	4	>	>	PUNCT
ap-7354	184	5	=	=	PUNCT
ap-7354	185	1	c±	c±	PROPN
ap-7354	185	2	n	n	CCONJ
ap-7354	185	3	|	|	ADV
ap-7354	185	4	n	n	CCONJ
ap-7354	185	5	;	;	PUNCT
ap-7354	185	6	1	1	NUM
ap-7354	185	7	2	2	NUM
ap-7354	185	8	>	>	X
ap-7354	185	9	+	+	NOUN
ap-7354	185	10	id±	id±	NOUN
ap-7354	185	11	n	n	NOUN
ap-7354	185	12	|	|	ADV
ap-7354	185	13	n−	n−	NOUN
ap-7354	185	14	1	1	NUM
ap-7354	185	15	;	;	PUNCT
ap-7354	185	16	−1	−1	NOUN
ap-7354	185	17	2	2	NUM
ap-7354	185	18	>	>	PUNCT
ap-7354	185	19	,	,	PUNCT
ap-7354	185	20	(	(	PUNCT
ap-7354	185	21	49	49	NUM
ap-7354	185	22	)	)	PUNCT
ap-7354	185	23	where	where	SCONJ
ap-7354	185	24	the	the	DET
ap-7354	185	25	coefficients	coefficient	NOUN
ap-7354	185	26	c±	c±	PROPN
ap-7354	185	27	n	n	PROPN
ap-7354	185	28	and	and	CCONJ
ap-7354	185	29	d±	d±	PROPN
ap-7354	185	30	n	n	NOUN
ap-7354	185	31	are	be	AUX
ap-7354	185	32	determined	determine	VERB
ap-7354	185	33	from	from	ADP
ap-7354	185	34	the	the	DET
ap-7354	185	35	normalization	normalization	NOUN
ap-7354	185	36	condition	condition	NOUN
ap-7354	185	37	.	.	PUNCT
ap-7354	186	1	we	we	PRON
ap-7354	186	2	thus	thus	ADV
ap-7354	186	3	obtain	obtain	VERB
ap-7354	186	4	[	[	X
ap-7354	186	5	24	24	NUM
ap-7354	186	6	]	]	X
ap-7354	186	7	c±	c±	PROPN
ap-7354	186	8	n	n	PROPN
ap-7354	186	9	=	=	PUNCT
ap-7354	186	10	√	√	PROPN
ap-7354	186	11	e+	e+	VERB
ap-7354	186	12	n	n	X
ap-7354	186	13	±mc2	±mc2	PROPN
ap-7354	186	14	2e+	2e+	NUM
ap-7354	186	15	n	n	NOUN
ap-7354	186	16	,	,	PUNCT
ap-7354	186	17	d±	d±	PROPN
ap-7354	186	18	n	n	NOUN
ap-7354	186	19	=	=	SYM
ap-7354	186	20	∓	∓	NOUN
ap-7354	186	21	√	√	NUM
ap-7354	186	22	e+	e+	VERB
ap-7354	186	23	n	n	X
ap-7354	186	24	∓mc2	∓mc2	PROPN
ap-7354	186	25	2e+	2e+	NUM
ap-7354	186	26	n	n	NOUN
ap-7354	186	27	.	.	PUNCT
ap-7354	187	1	(	(	PUNCT
ap-7354	187	2	50	50	NUM
ap-7354	187	3	)	)	PUNCT
ap-7354	187	4	in	in	ADP
ap-7354	187	5	the	the	DET
ap-7354	187	6	limit	limit	NOUN
ap-7354	187	7	θ	θ	X
ap-7354	187	8	→	→	SYM
ap-7354	187	9	0	0	NUM
ap-7354	187	10	,	,	PUNCT
ap-7354	187	11	the	the	DET
ap-7354	187	12	nc	nc	PROPN
ap-7354	187	13	energy	energy	PROPN
ap-7354	187	14	spectrum	spectrum	NOUN
ap-7354	187	15	becomes	become	VERB
ap-7354	187	16	commutative	commutative	ADJ
ap-7354	187	17	one	one	NUM
ap-7354	187	18	,	,	PUNCT
ap-7354	187	19	i.e.	i.e.	X
ap-7354	187	20	,	,	PUNCT
ap-7354	187	21	equation	equation	NOUN
ap-7354	187	22	(	(	PUNCT
ap-7354	187	23	47	47	NUM
ap-7354	187	24	)	)	PUNCT
ap-7354	187	25	turns	turn	VERB
ap-7354	187	26	to	to	ADP
ap-7354	187	27	equation	equation	NOUN
ap-7354	187	28	(	(	PUNCT
ap-7354	187	29	10	10	NUM
ap-7354	187	30	)	)	PUNCT
ap-7354	187	31	of	of	ADP
ap-7354	187	32	ref	ref	NOUN
ap-7354	187	33	.	.	PUNCT
ap-7354	188	1	[	[	X
ap-7354	188	2	32	32	NUM
ap-7354	188	3	]	]	PUNCT
ap-7354	188	4	,	,	PUNCT
ap-7354	188	5	which	which	PRON
ap-7354	188	6	confirms	confirm	VERB
ap-7354	188	7	that	that	SCONJ
ap-7354	188	8	we	we	PRON
ap-7354	188	9	are	be	AUX
ap-7354	188	10	in	in	ADP
ap-7354	188	11	good	good	ADJ
ap-7354	188	12	agreement	agreement	NOUN
ap-7354	188	13	.	.	PUNCT
ap-7354	189	1	as	as	ADV
ap-7354	189	2	well	well	ADV
ap-7354	189	3	,	,	PUNCT
ap-7354	189	4	in	in	ADP
ap-7354	189	5	ref	ref	NOUN
ap-7354	189	6	.	.	PUNCT
ap-7354	190	1	[	[	X
ap-7354	190	2	33	33	NUM
ap-7354	190	3	]	]	PUNCT
ap-7354	190	4	boumali	boumali	VERB
ap-7354	190	5	et	et	PROPN
ap-7354	190	6	al	al	PROPN
ap-7354	190	7	.	.	PROPN
ap-7354	190	8	made	make	VERB
ap-7354	190	9	a	a	DET
ap-7354	190	10	study	study	NOUN
ap-7354	190	11	of	of	ADP
ap-7354	190	12	a	a	DET
ap-7354	190	13	do	do	NOUN
ap-7354	190	14	in	in	ADP
ap-7354	190	15	an	an	DET
ap-7354	190	16	nc	nc	PROPN
ap-7354	190	17	phase	phase	NOUN
ap-7354	190	18	-	-	PUNCT
ap-7354	190	19	space	space	NOUN
ap-7354	190	20	,	,	PUNCT
ap-7354	190	21	where	where	SCONJ
ap-7354	190	22	,	,	PUNCT
ap-7354	190	23	if	if	SCONJ
ap-7354	190	24	θ	θ	PROPN
ap-7354	190	25	→	→	SYM
ap-7354	190	26	0	0	NUM
ap-7354	190	27	,	,	PUNCT
ap-7354	190	28	the	the	DET
ap-7354	190	29	energy	energy	NOUN
ap-7354	190	30	eigenvalues	eigenvalue	NOUN
ap-7354	190	31	(	(	PUNCT
ap-7354	190	32	eq:50	eq:50	PROPN
ap-7354	190	33	)	)	PUNCT
ap-7354	190	34	will	will	AUX
ap-7354	190	35	be	be	AUX
ap-7354	190	36	similar	similar	ADJ
ap-7354	190	37	as	as	ADP
ap-7354	190	38	ours	our	NOUN
ap-7354	190	39	in	in	ADP
ap-7354	190	40	equation	equation	NOUN
ap-7354	190	41	(	(	PUNCT
ap-7354	190	42	47	47	NUM
ap-7354	190	43	)	)	PUNCT
ap-7354	190	44	.	.	PUNCT
ap-7354	191	1	695	695	NUM
ap-7354	191	2	ilyas	ilyas	PROPN
ap-7354	191	3	haouam	haouam	PROPN
ap-7354	191	4	acta	acta	PROPN
ap-7354	191	5	polytechnica	polytechnica	PROPN
ap-7354	191	6	we	we	PRON
ap-7354	191	7	plot	plot	VERB
ap-7354	191	8	the	the	DET
ap-7354	191	9	reduced	reduce	VERB
ap-7354	191	10	energy	energy	NOUN
ap-7354	191	11	spectrum	spectrum	NOUN
ap-7354	191	12	in	in	ADP
ap-7354	191	13	terms	term	NOUN
ap-7354	191	14	of	of	ADP
ap-7354	191	15	quantum	quantum	ADJ
ap-7354	191	16	number	number	NOUN
ap-7354	191	17	n	n	CCONJ
ap-7354	191	18	,	,	PUNCT
ap-7354	191	19	for	for	ADP
ap-7354	191	20	the	the	DET
ap-7354	191	21	cases	case	NOUN
ap-7354	191	22	w	w	NOUN
ap-7354	191	23	=	=	SYM
ap-7354	191	24	1	1	NUM
ap-7354	191	25	,	,	PUNCT
ap-7354	191	26	q	q	NOUN
ap-7354	191	27	=	=	NOUN
ap-7354	191	28	1	1	NUM
ap-7354	191	29	;	;	PUNCT
ap-7354	191	30	w	w	NOUN
ap-7354	191	31	=	=	SYM
ap-7354	191	32	1	1	NUM
ap-7354	191	33	,	,	PUNCT
ap-7354	191	34	q	q	NOUN
ap-7354	191	35	=	=	SYM
ap-7354	191	36	2	2	NUM
ap-7354	191	37	and	and	CCONJ
ap-7354	191	38	the	the	DET
ap-7354	191	39	commutative	commutative	ADJ
ap-7354	191	40	case	case	NOUN
ap-7354	191	41	with	with	ADP
ap-7354	191	42	w	w	NOUN
ap-7354	191	43	=	=	SYM
ap-7354	191	44	1	1	NUM
ap-7354	191	45	.	.	PUNCT
ap-7354	192	1	the	the	DET
ap-7354	192	2	e±	e±	PROPN
ap-7354	192	3	n	n	DET
ap-7354	192	4	e0	e0	PROPN
ap-7354	192	5	,	,	PUNCT
ap-7354	192	6	as	as	ADP
ap-7354	192	7	a	a	DET
ap-7354	192	8	function	function	NOUN
ap-7354	192	9	of	of	ADP
ap-7354	192	10	quantum	quantum	ADJ
ap-7354	192	11	number	number	NOUN
ap-7354	192	12	n	n	NUM
ap-7354	192	13	of	of	ADP
ap-7354	192	14	equation	equation	NOUN
ap-7354	192	15	(	(	PUNCT
ap-7354	192	16	48	48	NUM
ap-7354	192	17	)	)	PUNCT
ap-7354	192	18	in	in	ADP
ap-7354	192	19	both	both	CCONJ
ap-7354	192	20	commutative	commutative	ADJ
ap-7354	192	21	(	(	PUNCT
ap-7354	192	22	θ	θ	NOUN
ap-7354	192	23	=	=	PUNCT
ap-7354	192	24	q	q	PROPN
ap-7354	192	25	=	=	NOUN
ap-7354	192	26	0	0	NUM
ap-7354	192	27	)	)	PUNCT
ap-7354	192	28	and	and	CCONJ
ap-7354	192	29	nc	nc	PROPN
ap-7354	192	30	(	(	PUNCT
ap-7354	192	31	q	q	NOUN
ap-7354	192	32	=	=	NOUN
ap-7354	192	33	1	1	NUM
ap-7354	192	34	;	;	PUNCT
ap-7354	192	35	q	q	NOUN
ap-7354	192	36	=	=	SYM
ap-7354	192	37	2	2	NUM
ap-7354	192	38	)	)	PUNCT
ap-7354	192	39	spaces	space	NOUN
ap-7354	192	40	,	,	PUNCT
ap-7354	192	41	is	be	AUX
ap-7354	192	42	illustrated	illustrate	VERB
ap-7354	192	43	in	in	ADP
ap-7354	192	44	fig	fig	NOUN
ap-7354	192	45	.	.	PUNCT
ap-7354	193	1	1	1	X
ap-7354	193	2	.	.	X
ap-7354	193	3	knowing	know	VERB
ap-7354	193	4	that	that	DET
ap-7354	193	5	fig	fig	NOUN
ap-7354	193	6	.	.	PUNCT
ap-7354	194	1	1	1	NUM
ap-7354	194	2	discloses	disclose	VERB
ap-7354	194	3	that	that	SCONJ
ap-7354	194	4	the	the	DET
ap-7354	194	5	influence	influence	NOUN
ap-7354	194	6	of	of	ADP
ap-7354	194	7	the	the	DET
ap-7354	194	8	nc	nc	PROPN
ap-7354	194	9	parameter	parameter	PROPN
ap-7354	194	10	on	on	ADP
ap-7354	194	11	the	the	DET
ap-7354	194	12	energy	energy	NOUN
ap-7354	194	13	spectrum	spectrum	NOUN
ap-7354	194	14	is	be	AUX
ap-7354	194	15	considerable	considerable	ADJ
ap-7354	194	16	and	and	CCONJ
ap-7354	194	17	significant	significant	ADJ
ap-7354	194	18	.	.	PUNCT
ap-7354	195	1	figure	figure	NOUN
ap-7354	195	2	1	1	NUM
ap-7354	195	3	.	.	PUNCT
ap-7354	196	1	a	a	DET
ap-7354	196	2	reduced	reduced	ADJ
ap-7354	196	3	energy	energy	NOUN
ap-7354	196	4	versus	versus	ADP
ap-7354	196	5	quantum	quantum	ADJ
ap-7354	196	6	number	number	NOUN
ap-7354	196	7	in	in	ADP
ap-7354	196	8	both	both	DET
ap-7354	196	9	cases	case	NOUN
ap-7354	196	10	of	of	ADP
ap-7354	196	11	nc	nc	PROPN
ap-7354	196	12	and	and	CCONJ
ap-7354	196	13	commutative	commutative	ADJ
ap-7354	196	14	spaces	space	NOUN
ap-7354	196	15	.	.	PUNCT
ap-7354	197	1	the	the	DET
ap-7354	197	2	following	follow	VERB
ap-7354	197	3	figure	figure	NOUN
ap-7354	197	4	shows	show	VERB
ap-7354	197	5	the	the	DET
ap-7354	197	6	coupling	coupling	NOUN
ap-7354	197	7	parameters	parameter	NOUN
ap-7354	197	8	g	g	PROPN
ap-7354	197	9	and	and	CCONJ
ap-7354	197	10	ḡ	ḡ	VERB
ap-7354	197	11	,	,	PUNCT
ap-7354	197	12	between	between	ADP
ap-7354	197	13	different	different	ADJ
ap-7354	197	14	levels	level	NOUN
ap-7354	197	15	for	for	ADP
ap-7354	197	16	the	the	DET
ap-7354	197	17	two	two	NUM
ap-7354	197	18	cases	case	NOUN
ap-7354	197	19	in	in	ADP
ap-7354	197	20	the	the	DET
ap-7354	197	21	nc	nc	PROPN
ap-7354	197	22	space	space	PROPN
ap-7354	197	23	.	.	PUNCT
ap-7354	198	1	figure	figure	NOUN
ap-7354	198	2	2	2	NUM
ap-7354	198	3	.	.	PUNCT
ap-7354	199	1	the	the	DET
ap-7354	199	2	coupling	couple	VERB
ap-7354	199	3	parameter	parameter	NOUN
ap-7354	199	4	between	between	ADP
ap-7354	199	5	different	different	ADJ
ap-7354	199	6	levels	level	NOUN
ap-7354	199	7	:	:	PUNCT
ap-7354	199	8	(	(	PUNCT
ap-7354	199	9	a	a	X
ap-7354	199	10	)	)	PUNCT
ap-7354	199	11	in	in	ADP
ap-7354	199	12	the	the	DET
ap-7354	199	13	case	case	NOUN
ap-7354	199	14	of	of	ADP
ap-7354	199	15	commutative	commutative	ADJ
ap-7354	199	16	space	space	NOUN
ap-7354	199	17	,	,	PUNCT
ap-7354	199	18	(	(	PUNCT
ap-7354	199	19	b	b	X
ap-7354	199	20	)	)	PUNCT
ap-7354	199	21	in	in	ADP
ap-7354	199	22	the	the	DET
ap-7354	199	23	case	case	NOUN
ap-7354	199	24	of	of	ADP
ap-7354	199	25	nc	nc	PROPN
ap-7354	199	26	space	space	NOUN
ap-7354	199	27	.	.	PUNCT
ap-7354	200	1	while	while	SCONJ
ap-7354	200	2	n	n	NOUN
ap-7354	200	3	are	be	AUX
ap-7354	200	4	non	non	ADJ
ap-7354	200	5	-	-	ADJ
ap-7354	200	6	negative	negative	ADJ
ap-7354	200	7	integers	integer	NOUN
ap-7354	200	8	,	,	PUNCT
ap-7354	200	9	we	we	PRON
ap-7354	200	10	explicitly	explicitly	ADV
ap-7354	200	11	observe	observe	VERB
ap-7354	200	12	that	that	SCONJ
ap-7354	200	13	our	our	PRON
ap-7354	200	14	eigenvalues	eigenvalue	NOUN
ap-7354	200	15	are	be	AUX
ap-7354	200	16	non	non	ADJ
ap-7354	200	17	-	-	ADJ
ap-7354	200	18	degenerated	degenerated	ADJ
ap-7354	200	19	(	(	PUNCT
ap-7354	200	20	the	the	DET
ap-7354	200	21	spectrum	spectrum	NOUN
ap-7354	200	22	has	have	AUX
ap-7354	200	23	no	no	DET
ap-7354	200	24	degeneracy	degeneracy	NOUN
ap-7354	200	25	)	)	PUNCT
ap-7354	200	26	,	,	PUNCT
ap-7354	200	27	this	this	DET
ap-7354	200	28	case	case	NOUN
ap-7354	200	29	can	can	AUX
ap-7354	200	30	be	be	AUX
ap-7354	200	31	explained	explain	VERB
ap-7354	200	32	by	by	ADP
ap-7354	200	33	the	the	DET
ap-7354	200	34	fact	fact	NOUN
ap-7354	200	35	that	that	SCONJ
ap-7354	200	36	the	the	DET
ap-7354	200	37	particle	particle	NOUN
ap-7354	200	38	is	be	AUX
ap-7354	200	39	restricted	restrict	VERB
ap-7354	200	40	to	to	ADP
ap-7354	200	41	moving	move	VERB
ap-7354	200	42	in	in	ADP
ap-7354	200	43	two	two	NUM
ap-7354	200	44	dimensions	dimension	NOUN
ap-7354	200	45	,	,	PUNCT
ap-7354	200	46	and	and	CCONJ
ap-7354	200	47	the	the	DET
ap-7354	200	48	third	third	ADJ
ap-7354	200	49	dimension	dimension	NOUN
ap-7354	200	50	does	do	AUX
ap-7354	200	51	not	not	PART
ap-7354	200	52	contribute	contribute	VERB
ap-7354	200	53	in	in	ADP
ap-7354	200	54	the	the	DET
ap-7354	200	55	form	form	NOUN
ap-7354	200	56	of	of	ADP
ap-7354	200	57	energy	energy	NOUN
ap-7354	200	58	.	.	PUNCT
ap-7354	201	1	knowing	know	VERB
ap-7354	201	2	that	that	PRON
ap-7354	201	3	,	,	PUNCT
ap-7354	201	4	it	it	PRON
ap-7354	201	5	will	will	AUX
ap-7354	201	6	be	be	AUX
ap-7354	201	7	an	an	DET
ap-7354	201	8	infinite	infinite	ADJ
ap-7354	201	9	degeneracy	degeneracy	NOUN
ap-7354	201	10	when	when	SCONJ
ap-7354	201	11	there	there	PRON
ap-7354	201	12	is	be	VERB
ap-7354	201	13	a	a	DET
ap-7354	201	14	contribution	contribution	NOUN
ap-7354	201	15	of	of	ADP
ap-7354	201	16	an	an	DET
ap-7354	201	17	element	element	NOUN
ap-7354	201	18	related	relate	VERB
ap-7354	201	19	to	to	ADP
ap-7354	201	20	the	the	DET
ap-7354	201	21	third	third	ADJ
ap-7354	201	22	dimension	dimension	NOUN
ap-7354	201	23	,	,	PUNCT
ap-7354	201	24	such	such	ADJ
ap-7354	201	25	as	as	ADP
ap-7354	201	26	kz	kz	PROPN
ap-7354	201	27	or	or	CCONJ
ap-7354	201	28	pz	pz	PROPN
ap-7354	201	29	.	.	PROPN
ap-7354	201	30	in	in	ADP
ap-7354	201	31	more	more	ADJ
ap-7354	201	32	detail	detail	NOUN
ap-7354	201	33	and	and	CCONJ
ap-7354	201	34	indirectly	indirectly	ADV
ap-7354	201	35	(	(	PUNCT
ap-7354	201	36	in	in	ADP
ap-7354	201	37	other	other	ADJ
ap-7354	201	38	sense	sense	NOUN
ap-7354	201	39	)	)	PUNCT
ap-7354	201	40	,	,	PUNCT
ap-7354	201	41	the	the	DET
ap-7354	201	42	energy	energy	NOUN
ap-7354	201	43	spectrum	spectrum	NOUN
ap-7354	201	44	is	be	AUX
ap-7354	201	45	degenerated	degenerated	ADJ
ap-7354	201	46	.	.	PUNCT
ap-7354	202	1	as	as	SCONJ
ap-7354	202	2	is	be	AUX
ap-7354	202	3	known	know	VERB
ap-7354	202	4	,	,	PUNCT
ap-7354	202	5	this	this	PRON
ap-7354	202	6	is	be	AUX
ap-7354	202	7	related	relate	VERB
ap-7354	202	8	to	to	ADP
ap-7354	202	9	the	the	DET
ap-7354	202	10	landau	landau	NOUN
ap-7354	202	11	problem	problem	NOUN
ap-7354	202	12	,	,	PUNCT
ap-7354	202	13	and	and	CCONJ
ap-7354	202	14	it	it	PRON
ap-7354	202	15	is	be	AUX
ap-7354	202	16	known	know	VERB
ap-7354	202	17	that	that	SCONJ
ap-7354	202	18	there	there	PRON
ap-7354	202	19	is	be	VERB
ap-7354	202	20	an	an	DET
ap-7354	202	21	infinite	infinite	ADJ
ap-7354	202	22	degeneracy	degeneracy	NOUN
ap-7354	202	23	.	.	PUNCT
ap-7354	203	1	nevertheless	nevertheless	ADV
ap-7354	203	2	,	,	PUNCT
ap-7354	203	3	we	we	PRON
ap-7354	203	4	consider	consider	VERB
ap-7354	203	5	the	the	DET
ap-7354	203	6	energy	energy	NOUN
ap-7354	203	7	spectrum	spectrum	NOUN
ap-7354	203	8	non	non	ADJ
ap-7354	203	9	-	-	ADJ
ap-7354	203	10	degenerated	degenerated	ADJ
ap-7354	203	11	,	,	PUNCT
ap-7354	203	12	because	because	SCONJ
ap-7354	203	13	we	we	PRON
ap-7354	203	14	do	do	AUX
ap-7354	203	15	not	not	PART
ap-7354	203	16	rely	rely	VERB
ap-7354	203	17	on	on	ADP
ap-7354	203	18	the	the	DET
ap-7354	203	19	states	state	NOUN
ap-7354	203	20	with	with	ADP
ap-7354	203	21	different	different	ADJ
ap-7354	203	22	angular	angular	ADJ
ap-7354	203	23	momentum	momentum	NOUN
ap-7354	203	24	,	,	PUNCT
ap-7354	203	25	which	which	PRON
ap-7354	203	26	is	be	AUX
ap-7354	203	27	not	not	PART
ap-7354	203	28	useful	useful	ADJ
ap-7354	203	29	here	here	ADV
ap-7354	203	30	.	.	PUNCT
ap-7354	204	1	the	the	DET
ap-7354	204	2	reason	reason	NOUN
ap-7354	204	3	is	be	AUX
ap-7354	204	4	that	that	SCONJ
ap-7354	204	5	when	when	SCONJ
ap-7354	204	6	we	we	PRON
ap-7354	204	7	use	use	VERB
ap-7354	204	8	chiral	chiral	ADJ
ap-7354	204	9	creation	creation	NOUN
ap-7354	204	10	and	and	CCONJ
ap-7354	204	11	annihilation	annihilation	NOUN
ap-7354	204	12	operators	operator	NOUN
ap-7354	204	13	(	(	PUNCT
ap-7354	204	14	al	al	PROPN
ap-7354	204	15	,	,	PUNCT
ap-7354	204	16	a†	a†	NOUN
ap-7354	204	17	l	l	PROPN
ap-7354	204	18	and	and	CCONJ
ap-7354	204	19	ar	ar	PROPN
ap-7354	204	20	,	,	PUNCT
ap-7354	204	21	a†	a†	NOUN
ap-7354	204	22	r	r	NOUN
ap-7354	204	23	)	)	PUNCT
ap-7354	204	24	,	,	PUNCT
ap-7354	204	25	we	we	PRON
ap-7354	204	26	see	see	VERB
ap-7354	204	27	that	that	SCONJ
ap-7354	204	28	the	the	DET
ap-7354	204	29	number	number	NOUN
ap-7354	204	30	of	of	ADP
ap-7354	204	31	particles	particle	NOUN
ap-7354	204	32	nr	nr	PRON
ap-7354	204	33	created	create	VERB
ap-7354	204	34	by	by	ADP
ap-7354	204	35	right	right	ADJ
ap-7354	204	36	operators	operator	NOUN
ap-7354	204	37	does	do	AUX
ap-7354	204	38	not	not	PART
ap-7354	204	39	appear	appear	VERB
ap-7354	204	40	in	in	ADP
ap-7354	204	41	the	the	DET
ap-7354	204	42	form	form	NOUN
ap-7354	204	43	of	of	ADP
ap-7354	204	44	energy	energy	NOUN
ap-7354	204	45	,	,	PUNCT
ap-7354	204	46	we	we	PRON
ap-7354	204	47	see	see	VERB
ap-7354	204	48	only	only	ADV
ap-7354	204	49	number	number	NOUN
ap-7354	204	50	of	of	ADP
ap-7354	204	51	particles	particle	NOUN
ap-7354	204	52	nl	nl	PROPN
ap-7354	204	53	generated	generate	VERB
ap-7354	204	54	by	by	ADP
ap-7354	204	55	left	left	ADJ
ap-7354	204	56	operators	operator	NOUN
ap-7354	204	57	.	.	PUNCT
ap-7354	205	1	however	however	ADV
ap-7354	205	2	,	,	PUNCT
ap-7354	205	3	right	right	ADJ
ap-7354	205	4	operators	operator	NOUN
ap-7354	205	5	create	create	VERB
ap-7354	205	6	excitations	excitation	NOUN
ap-7354	205	7	with	with	ADP
ap-7354	205	8	a	a	DET
ap-7354	205	9	definite	definite	ADJ
ap-7354	205	10	angular	angular	ADJ
ap-7354	205	11	momentum	momentum	NOUN
ap-7354	205	12	in	in	ADP
ap-7354	205	13	one	one	NUM
ap-7354	205	14	or	or	CCONJ
ap-7354	205	15	the	the	DET
ap-7354	205	16	other	other	ADJ
ap-7354	205	17	direction	direction	NOUN
ap-7354	205	18	;	;	PUNCT
ap-7354	205	19	thus	thus	ADV
ap-7354	205	20	,	,	PUNCT
ap-7354	205	21	in	in	ADP
ap-7354	205	22	this	this	DET
ap-7354	205	23	sense	sense	NOUN
ap-7354	205	24	,	,	PUNCT
ap-7354	205	25	we	we	PRON
ap-7354	205	26	have	have	VERB
ap-7354	205	27	the	the	DET
ap-7354	205	28	degeneracy	degeneracy	NOUN
ap-7354	205	29	.	.	PUNCT
ap-7354	206	1	this	this	DET
ap-7354	206	2	point	point	NOUN
ap-7354	206	3	is	be	AUX
ap-7354	206	4	very	very	ADV
ap-7354	206	5	important	important	ADJ
ap-7354	206	6	to	to	PART
ap-7354	206	7	clarify	clarify	VERB
ap-7354	206	8	because	because	SCONJ
ap-7354	206	9	our	our	PRON
ap-7354	206	10	calculations	calculation	NOUN
ap-7354	206	11	in	in	ADP
ap-7354	206	12	the	the	DET
ap-7354	206	13	perturbation	perturbation	NOUN
ap-7354	206	14	theory	theory	NOUN
ap-7354	206	15	depend	depend	VERB
ap-7354	206	16	on	on	ADP
ap-7354	206	17	this	this	DET
ap-7354	206	18	point	point	NOUN
ap-7354	206	19	.	.	PUNCT
ap-7354	207	1	as	as	SCONJ
ap-7354	207	2	many	many	ADJ
ap-7354	207	3	researchers	researcher	NOUN
ap-7354	207	4	have	have	AUX
ap-7354	207	5	dealt	deal	VERB
ap-7354	207	6	with	with	ADP
ap-7354	207	7	this	this	DET
ap-7354	207	8	sensitive	sensitive	ADJ
ap-7354	207	9	point	point	NOUN
ap-7354	207	10	and	and	CCONJ
ap-7354	207	11	considered	consider	VERB
ap-7354	207	12	that	that	SCONJ
ap-7354	207	13	the	the	DET
ap-7354	207	14	spectrum	spectrum	NOUN
ap-7354	207	15	has	have	VERB
ap-7354	207	16	no	no	DET
ap-7354	207	17	degeneracy	degeneracy	NOUN
ap-7354	207	18	such	such	ADJ
ap-7354	207	19	as	as	ADP
ap-7354	207	20	[	[	X
ap-7354	207	21	33	33	NUM
ap-7354	207	22	]	]	PUNCT
ap-7354	207	23	.	.	PUNCT
ap-7354	208	1	besides	besides	SCONJ
ap-7354	208	2	,	,	PUNCT
ap-7354	208	3	differently	differently	ADV
ap-7354	208	4	,	,	PUNCT
ap-7354	208	5	for	for	ADP
ap-7354	208	6	instance	instance	NOUN
ap-7354	208	7	,	,	PUNCT
ap-7354	208	8	energy	energy	NOUN
ap-7354	208	9	levels	level	NOUN
ap-7354	208	10	can	can	AUX
ap-7354	208	11	appear	appear	VERB
ap-7354	208	12	explicitly	explicitly	ADV
ap-7354	208	13	degenerated	degenerated	ADJ
ap-7354	208	14	,	,	PUNCT
ap-7354	208	15	as	as	ADP
ap-7354	208	16	in	in	ADP
ap-7354	208	17	a	a	DET
ap-7354	208	18	study	study	NOUN
ap-7354	208	19	[	[	X
ap-7354	208	20	34	34	NUM
ap-7354	208	21	]	]	PUNCT
ap-7354	208	22	about	about	ADP
ap-7354	208	23	the	the	DET
ap-7354	208	24	mesoscopic	mesoscopic	NOUN
ap-7354	208	25	states	state	NOUN
ap-7354	208	26	in	in	ADP
ap-7354	208	27	a	a	DET
ap-7354	208	28	relativistic	relativistic	ADJ
ap-7354	208	29	landau	landau	NOUN
ap-7354	208	30	levels	level	NOUN
ap-7354	208	31	,	,	PUNCT
ap-7354	208	32	the	the	DET
ap-7354	208	33	authors	author	NOUN
ap-7354	208	34	found	find	VERB
ap-7354	208	35	that	that	SCONJ
ap-7354	208	36	the	the	DET
ap-7354	208	37	energy	energy	NOUN
ap-7354	208	38	spectrum	spectrum	NOUN
ap-7354	208	39	depends	depend	VERB
ap-7354	208	40	on	on	ADP
ap-7354	208	41	p2	p2	PROPN
ap-7354	208	42	z	z	PROPN
ap-7354	208	43	(	(	PUNCT
ap-7354	208	44	check	check	VERB
ap-7354	208	45	eq	eq	ADP
ap-7354	208	46	.	.	PROPN
ap-7354	208	47	13	13	NUM
ap-7354	208	48	in	in	ADP
ap-7354	208	49	this	this	DET
ap-7354	208	50	cited	cite	VERB
ap-7354	208	51	reference	reference	NOUN
ap-7354	208	52	)	)	PUNCT
ap-7354	208	53	,	,	PUNCT
ap-7354	208	54	which	which	PRON
ap-7354	208	55	is	be	AUX
ap-7354	208	56	the	the	DET
ap-7354	208	57	underlying	underlying	ADJ
ap-7354	208	58	reason	reason	NOUN
ap-7354	208	59	for	for	ADP
ap-7354	208	60	an	an	DET
ap-7354	208	61	infinite	infinite	ADJ
ap-7354	208	62	degeneracy	degeneracy	NOUN
ap-7354	208	63	of	of	ADP
ap-7354	208	64	all	all	DET
ap-7354	208	65	levels	level	NOUN
ap-7354	208	66	.	.	PUNCT
ap-7354	209	1	3.3	3.3	NUM
ap-7354	209	2	.	.	PUNCT
ap-7354	209	3	perturbed	perturb	VERB
ap-7354	209	4	system	system	NOUN
ap-7354	209	5	in	in	ADP
ap-7354	209	6	this	this	DET
ap-7354	209	7	sub	sub	NOUN
ap-7354	209	8	-	-	NOUN
ap-7354	209	9	section	section	NOUN
ap-7354	209	10	,	,	PUNCT
ap-7354	209	11	we	we	PRON
ap-7354	209	12	aim	aim	VERB
ap-7354	209	13	to	to	PART
ap-7354	209	14	determine	determine	VERB
ap-7354	209	15	the	the	DET
ap-7354	209	16	correction	correction	NOUN
ap-7354	209	17	of	of	ADP
ap-7354	209	18	first	first	ADJ
ap-7354	209	19	-	-	PUNCT
ap-7354	209	20	order	order	NOUN
ap-7354	209	21	energy	energy	NOUN
ap-7354	209	22	by	by	ADP
ap-7354	209	23	using	use	VERB
ap-7354	209	24	first	first	ADJ
ap-7354	209	25	-	-	PUNCT
ap-7354	209	26	order	order	NOUN
ap-7354	209	27	energy	energy	NOUN
ap-7354	209	28	shift	shift	NOUN
ap-7354	209	29	formulas	formula	NOUN
ap-7354	209	30	.	.	PUNCT
ap-7354	210	1	to	to	PART
ap-7354	210	2	explain	explain	VERB
ap-7354	210	3	the	the	DET
ap-7354	210	4	structure	structure	NOUN
ap-7354	210	5	of	of	ADP
ap-7354	210	6	our	our	PRON
ap-7354	210	7	spectrum	spectrum	NOUN
ap-7354	210	8	,	,	PUNCT
ap-7354	210	9	we	we	PRON
ap-7354	210	10	will	will	AUX
ap-7354	210	11	use	use	VERB
ap-7354	210	12	time	time	NOUN
ap-7354	210	13	-	-	PUNCT
ap-7354	210	14	independent	independent	ADJ
ap-7354	210	15	perturbation	perturbation	NOUN
ap-7354	210	16	theory	theory	NOUN
ap-7354	210	17	for	for	ADP
ap-7354	210	18	696	696	NUM
ap-7354	210	19	vol	vol	NOUN
ap-7354	210	20	.	.	PUNCT
ap-7354	211	1	61	61	NUM
ap-7354	211	2	no	no	NOUN
ap-7354	211	3	.	.	PUNCT
ap-7354	212	1	6/2021	6/2021	NUM
ap-7354	212	2	dirac	dirac	NOUN
ap-7354	212	3	oscillator	oscillator	NOUN
ap-7354	212	4	in	in	ADP
ap-7354	212	5	dynamical	dynamical	ADJ
ap-7354	212	6	noncommutative	noncommutative	ADJ
ap-7354	212	7	space	space	NOUN
ap-7354	212	8	small	small	ADJ
ap-7354	212	9	values	value	NOUN
ap-7354	212	10	of	of	ADP
ap-7354	212	11	the	the	DET
ap-7354	212	12	parameter	parameter	NOUN
ap-7354	212	13	τ	τ	PROPN
ap-7354	212	14	.	.	PUNCT
ap-7354	213	1	in	in	ADP
ap-7354	213	2	view	view	NOUN
ap-7354	213	3	that	that	SCONJ
ap-7354	213	4	energies	energy	NOUN
ap-7354	213	5	are	be	AUX
ap-7354	213	6	non	non	ADJ
ap-7354	213	7	-	-	ADJ
ap-7354	213	8	degenerated	degenerated	ADJ
ap-7354	213	9	,	,	PUNCT
ap-7354	213	10	we	we	PRON
ap-7354	213	11	use	use	VERB
ap-7354	213	12	the	the	DET
ap-7354	213	13	non	non	ADJ
ap-7354	213	14	-	-	ADJ
ap-7354	213	15	degenerated	degenerated	ADJ
ap-7354	213	16	time	time	NOUN
ap-7354	213	17	-	-	PUNCT
ap-7354	213	18	independent	independent	ADJ
ap-7354	213	19	perturbation	perturbation	NOUN
ap-7354	213	20	theory	theory	NOUN
ap-7354	213	21	∣∣ψn	∣∣ψn	NOUN
ap-7354	213	22	〉	〉	NOUN
ap-7354	213	23	=	=	SYM
ap-7354	213	24	∣∣∣ψ(0	∣∣∣ψ(0	NOUN
ap-7354	213	25	)	)	PUNCT
ap-7354	214	1	n	n	CCONJ
ap-7354	214	2	〉	〉	NOUN
ap-7354	214	3	+	+	CCONJ
ap-7354	214	4	τ	τ	PROPN
ap-7354	214	5	∣∣∣ψ(1	∣∣∣ψ(1	PROPN
ap-7354	214	6	)	)	PUNCT
ap-7354	214	7	n	n	CCONJ
ap-7354	214	8	〉	〉	NOUN
ap-7354	214	9	+	+	CCONJ
ap-7354	214	10	τ2	τ2	PROPN
ap-7354	214	11	∣∣∣ψ(2	∣∣∣ψ(2	NOUN
ap-7354	214	12	)	)	PUNCT
ap-7354	214	13	n	n	CCONJ
ap-7354	214	14	〉	〉	NOUN
ap-7354	214	15	+	+	X
ap-7354	214	16	...	...	PUNCT
ap-7354	214	17	(	(	PUNCT
ap-7354	214	18	51	51	NUM
ap-7354	214	19	)	)	PUNCT
ap-7354	214	20	en	en	NOUN
ap-7354	214	21	=	=	SYM
ap-7354	214	22	e(0	e(0	NOUN
ap-7354	214	23	)	)	PUNCT
ap-7354	214	24	n	n	PROPN
ap-7354	214	25	+	+	CCONJ
ap-7354	214	26	τe(1	τe(1	NOUN
ap-7354	214	27	)	)	PUNCT
ap-7354	214	28	n	n	PRON
ap-7354	214	29	+	+	CCONJ
ap-7354	214	30	τ2e(2	τ2e(2	PROPN
ap-7354	214	31	)	)	PUNCT
ap-7354	214	32	n	n	PROPN
ap-7354	214	33	+	+	CCONJ
ap-7354	214	34	...	...	PUNCT
ap-7354	214	35	(	(	PUNCT
ap-7354	214	36	52	52	NUM
ap-7354	214	37	)	)	PUNCT
ap-7354	214	38	here	here	ADV
ap-7354	214	39	,	,	PUNCT
ap-7354	214	40	the	the	DET
ap-7354	214	41	(	(	PUNCT
ap-7354	214	42	0	0	NUM
ap-7354	214	43	)	)	PUNCT
ap-7354	214	44	superscript	superscript	NOUN
ap-7354	214	45	denotes	denote	VERB
ap-7354	214	46	the	the	DET
ap-7354	214	47	quantities	quantity	NOUN
ap-7354	214	48	that	that	PRON
ap-7354	214	49	are	be	AUX
ap-7354	214	50	associated	associate	VERB
ap-7354	214	51	with	with	ADP
ap-7354	214	52	the	the	DET
ap-7354	214	53	unperturbed	unperturbed	ADJ
ap-7354	214	54	system	system	NOUN
ap-7354	214	55	.	.	PUNCT
ap-7354	215	1	the	the	DET
ap-7354	215	2	first	first	ADJ
ap-7354	215	3	-	-	PUNCT
ap-7354	215	4	order	order	NOUN
ap-7354	215	5	correction	correction	NOUN
ap-7354	215	6	to	to	ADP
ap-7354	215	7	the	the	DET
ap-7354	215	8	eigenvalues	eigenvalue	NOUN
ap-7354	215	9	and	and	CCONJ
ap-7354	215	10	eigenvectors	eigenvector	NOUN
ap-7354	215	11	in	in	ADP
ap-7354	215	12	perturbation	perturbation	NOUN
ap-7354	215	13	theory	theory	NOUN
ap-7354	215	14	are	be	AUX
ap-7354	215	15	simply	simply	ADV
ap-7354	215	16	given	give	VERB
ap-7354	215	17	by	by	ADP
ap-7354	215	18	e(1	e(1	NOUN
ap-7354	215	19	)	)	PUNCT
ap-7354	215	20	n	n	NOUN
ap-7354	215	21	=	=	PUNCT
ap-7354	215	22	△	△	X
ap-7354	215	23	en	en	X
ap-7354	215	24	=	=	SYM
ap-7354	215	25	<	<	X
ap-7354	215	26	ψ	ψ	X
ap-7354	215	27	(	(	PUNCT
ap-7354	215	28	0	0	NUM
ap-7354	215	29	)	)	PUNCT
ap-7354	215	30	n	n	NOUN
ap-7354	215	31	|	|	ADV
ap-7354	215	32	1	1	NUM
ap-7354	215	33	τ	τ	NOUN
ap-7354	215	34	hτ	hτ	NOUN
ap-7354	215	35	|	|	ADV
ap-7354	215	36	ψ(0	ψ(0	NOUN
ap-7354	215	37	)	)	PUNCT
ap-7354	215	38	n	n	CCONJ
ap-7354	215	39	>	>	PUNCT
ap-7354	215	40	,	,	PUNCT
ap-7354	215	41	(	(	PUNCT
ap-7354	215	42	53	53	NUM
ap-7354	215	43	)	)	PUNCT
ap-7354	215	44	∣∣∣ψ(1	∣∣∣ψ(1	PROPN
ap-7354	215	45	)	)	PUNCT
ap-7354	215	46	n	n	PRON
ap-7354	215	47	〉	〉	NOUN
ap-7354	215	48	=	=	SYM
ap-7354	215	49	∑	∑	PUNCT
ap-7354	215	50	k	k	X
ap-7354	215	51	̸=n	̸=n	X
ap-7354	215	52	<	<	X
ap-7354	215	53	ψ	ψ	X
ap-7354	215	54	(	(	PUNCT
ap-7354	215	55	0	0	NUM
ap-7354	215	56	)	)	PUNCT
ap-7354	215	57	k	k	NOUN
ap-7354	216	1	|	|	ADV
ap-7354	216	2	1	1	NUM
ap-7354	216	3	τhτ	τhτ	NOUN
ap-7354	216	4	|	|	ADV
ap-7354	216	5	ψ(0	ψ(0	NOUN
ap-7354	216	6	)	)	PUNCT
ap-7354	216	7	n	n	CCONJ
ap-7354	216	8	>	>	X
ap-7354	216	9	e	e	X
ap-7354	216	10	(	(	PUNCT
ap-7354	216	11	0	0	NUM
ap-7354	216	12	)	)	PUNCT
ap-7354	216	13	n	n	CCONJ
ap-7354	216	14	−	−	PROPN
ap-7354	216	15	e	e	X
ap-7354	216	16	(	(	PUNCT
ap-7354	216	17	0	0	NUM
ap-7354	216	18	)	)	PUNCT
ap-7354	216	19	k	k	PROPN
ap-7354	216	20	∣∣∣ψ(0	∣∣∣ψ(0	PROPN
ap-7354	216	21	)	)	PUNCT
ap-7354	217	1	k	k	PROPN
ap-7354	217	2	〉	〉	NOUN
ap-7354	217	3	.	.	PUNCT
ap-7354	218	1	(	(	PUNCT
ap-7354	218	2	54	54	NUM
ap-7354	218	3	)	)	PUNCT
ap-7354	218	4	inserting	insert	VERB
ap-7354	218	5	equation	equation	NOUN
ap-7354	218	6	(	(	PUNCT
ap-7354	218	7	25	25	NUM
ap-7354	218	8	)	)	PUNCT
ap-7354	218	9	into	into	ADP
ap-7354	218	10	the	the	DET
ap-7354	218	11	equation	equation	NOUN
ap-7354	218	12	above	above	ADV
ap-7354	218	13	,	,	PUNCT
ap-7354	218	14	we	we	PRON
ap-7354	218	15	find	find	VERB
ap-7354	218	16	e(1	e(1	NOUN
ap-7354	218	17	)	)	PUNCT
ap-7354	218	18	n	n	NOUN
ap-7354	219	1	=	=	NUM
ap-7354	219	2	<	<	X
ap-7354	219	3	ψ	ψ	X
ap-7354	219	4	(	(	PUNCT
ap-7354	219	5	0	0	NUM
ap-7354	219	6	)	)	PUNCT
ap-7354	219	7	n	n	NOUN
ap-7354	219	8	|	|	ADV
ap-7354	219	9	1	1	NUM
ap-7354	219	10	2{α2(v1	2{α2(v1	NUM
ap-7354	219	11	+	+	NUM
ap-7354	219	12	v2	v2	NOUN
ap-7354	219	13	)	)	PUNCT
ap-7354	219	14	−	−	PROPN
ap-7354	219	15	(	(	PUNCT
ap-7354	219	16	ebα2	ebα2	PROPN
ap-7354	219	17	+	+	CCONJ
ap-7354	219	18	i2mcωα1β	i2mcωα1β	PROPN
ap-7354	219	19	)	)	PUNCT
ap-7354	219	20	v3	v3	PROPN
ap-7354	219	21	}	}	PUNCT
ap-7354	219	22	|	|	ADV
ap-7354	219	23	ψ(0	ψ(0	NOUN
ap-7354	219	24	)	)	PUNCT
ap-7354	219	25	n	n	CCONJ
ap-7354	219	26	>	>	PUNCT
ap-7354	219	27	,	,	PUNCT
ap-7354	220	1	(	(	PUNCT
ap-7354	220	2	55	55	NUM
ap-7354	220	3	)	)	PUNCT
ap-7354	220	4	the	the	DET
ap-7354	220	5	operator	operator	NOUN
ap-7354	220	6	method	method	NOUN
ap-7354	220	7	can	can	AUX
ap-7354	220	8	also	also	ADV
ap-7354	220	9	be	be	AUX
ap-7354	220	10	used	use	VERB
ap-7354	220	11	to	to	PART
ap-7354	220	12	obtain	obtain	VERB
ap-7354	220	13	the	the	DET
ap-7354	220	14	energy	energy	NOUN
ap-7354	220	15	shift	shift	NOUN
ap-7354	220	16	in	in	ADP
ap-7354	220	17	fock	fock	ADJ
ap-7354	220	18	space	space	NOUN
ap-7354	220	19	.	.	PUNCT
ap-7354	221	1	in	in	ADP
ap-7354	221	2	our	our	PRON
ap-7354	221	3	scenario	scenario	NOUN
ap-7354	221	4	,	,	PUNCT
ap-7354	221	5	we	we	PRON
ap-7354	221	6	require	require	VERB
ap-7354	221	7	adopting	adopt	VERB
ap-7354	221	8	the	the	DET
ap-7354	221	9	notation	notation	NOUN
ap-7354	221	10	of	of	ADP
ap-7354	221	11	the	the	DET
ap-7354	221	12	state	state	NOUN
ap-7354	221	13	as	as	SCONJ
ap-7354	221	14	follows	follow	VERB
ap-7354	221	15	|	|	ADV
ap-7354	221	16	ψ(0	ψ(0	NOUN
ap-7354	221	17	)	)	PUNCT
ap-7354	221	18	n	n	CCONJ
ap-7354	221	19	>	>	PUNCT
ap-7354	221	20	=|	=|	X
ap-7354	221	21	nx	nx	PROPN
ap-7354	221	22	,	,	PUNCT
ap-7354	221	23	ny	ny	PROPN
ap-7354	221	24	>	>	X
ap-7354	221	25	.	.	PUNCT
ap-7354	222	1	(	(	PUNCT
ap-7354	222	2	56	56	NUM
ap-7354	222	3	)	)	PUNCT
ap-7354	222	4	the	the	DET
ap-7354	222	5	perturbation	perturbation	NOUN
ap-7354	222	6	matrix	matrix	NOUN
ap-7354	222	7	is	be	AUX
ap-7354	222	8	given	give	VERB
ap-7354	222	9	by	by	ADP
ap-7354	222	10	m	m	NOUN
ap-7354	222	11	=	=	NOUN
ap-7354	222	12	<	<	X
ap-7354	222	13	nx	nx	X
ap-7354	222	14	,	,	PUNCT
ap-7354	222	15	ny	ny	PROPN
ap-7354	222	16	|	|	PROPN
ap-7354	222	17	i2	i2	PROPN
ap-7354	222	18	(	(	PUNCT
ap-7354	222	19	0	0	NUM
ap-7354	222	20	−v1	−v1	PROPN
ap-7354	222	21	−	−	PROPN
ap-7354	223	1	v2	v2	NOUN
ap-7354	224	1	+	+	CCONJ
ap-7354	224	2	υv3	υv3	PROPN
ap-7354	224	3	v1	v1	PROPN
ap-7354	224	4	+	+	CCONJ
ap-7354	224	5	v2	v2	PROPN
ap-7354	224	6	−	−	PROPN
ap-7354	224	7	υv3	υv3	NOUN
ap-7354	224	8	0	0	NUM
ap-7354	224	9	)	)	PUNCT
ap-7354	225	1	|	|	ADV
ap-7354	225	2	n	n	ADV
ap-7354	225	3	′	′	NUM
ap-7354	226	1	x	x	NOUN
ap-7354	226	2	,	,	PUNCT
ap-7354	226	3	n	n	PROPN
ap-7354	226	4	′	′	NOUN
ap-7354	227	1	y	y	NOUN
ap-7354	227	2	>	>	PUNCT
ap-7354	227	3	,	,	PUNCT
ap-7354	227	4	(	(	PUNCT
ap-7354	227	5	57	57	NUM
ap-7354	227	6	)	)	PUNCT
ap-7354	227	7	with	with	ADP
ap-7354	227	8	υ	υ	PROPN
ap-7354	227	9	=	=	PUNCT
ap-7354	227	10	eb	eb	PROPN
ap-7354	227	11	+	+	PROPN
ap-7354	227	12	2mcω	2mcω	NUM
ap-7354	227	13	.	.	PUNCT
ap-7354	228	1	to	to	PART
ap-7354	228	2	calculate	calculate	VERB
ap-7354	228	3	the	the	DET
ap-7354	228	4	influence	influence	NOUN
ap-7354	228	5	of	of	ADP
ap-7354	228	6	vi	vi	PROPN
ap-7354	228	7	(	(	PUNCT
ap-7354	228	8	i	i	NOUN
ap-7354	228	9	=	=	NOUN
ap-7354	228	10	1	1	NUM
ap-7354	228	11	,	,	PUNCT
ap-7354	228	12	..	..	PUNCT
ap-7354	228	13	,	,	PUNCT
ap-7354	228	14	3	3	X
ap-7354	228	15	)	)	PUNCT
ap-7354	228	16	on	on	ADP
ap-7354	228	17	the	the	DET
ap-7354	228	18	element	element	NOUN
ap-7354	228	19	of	of	ADP
ap-7354	228	20	the	the	DET
ap-7354	228	21	fock	fock	ADJ
ap-7354	228	22	basis	basis	NOUN
ap-7354	228	23	,	,	PUNCT
ap-7354	228	24	we	we	PRON
ap-7354	228	25	conveniently	conveniently	ADV
ap-7354	228	26	use	use	VERB
ap-7354	228	27	the	the	DET
ap-7354	228	28	following	follow	VERB
ap-7354	228	29	bj	bj	NOUN
ap-7354	228	30	,	,	PUNCT
ap-7354	228	31	b†	b†	PROPN
ap-7354	228	32	j	j	PROPN
ap-7354	228	33	(	(	PUNCT
ap-7354	228	34	j	j	PROPN
ap-7354	228	35	=	=	SYM
ap-7354	228	36	x	x	PROPN
ap-7354	228	37	,	,	PUNCT
ap-7354	228	38	y	y	NOUN
ap-7354	228	39	)	)	PUNCT
ap-7354	228	40	operators	operator	NOUN
ap-7354	228	41	bj	bj	VERB
ap-7354	228	42	=	=	PUNCT
ap-7354	228	43	√	√	NUM
ap-7354	228	44	mω	mω	NOUN
ap-7354	228	45	2ℏ	2ℏ	NUM
ap-7354	228	46	(	(	PUNCT
ap-7354	228	47	xs	xs	PROPN
ap-7354	228	48	j	j	PROPN
ap-7354	229	1	+	+	CCONJ
ap-7354	229	2	i	i	PRON
ap-7354	229	3	ps	ps	VERB
ap-7354	229	4	j	j	NOUN
ap-7354	229	5	mω	mω	PROPN
ap-7354	229	6	)	)	PUNCT
ap-7354	229	7	and	and	CCONJ
ap-7354	229	8	b†	b†	PROPN
ap-7354	229	9	j	j	PROPN
ap-7354	230	1	=	=	PUNCT
ap-7354	230	2	√	√	NUM
ap-7354	230	3	mω	mω	VERB
ap-7354	230	4	2ℏ	2ℏ	NUM
ap-7354	230	5	(	(	PUNCT
ap-7354	230	6	xs	xs	PROPN
ap-7354	230	7	j	j	PROPN
ap-7354	231	1	−	−	PROPN
ap-7354	232	1	i	i	PRON
ap-7354	232	2	ps	ps	VERB
ap-7354	232	3	j	j	PROPN
ap-7354	232	4	mω	mω	PROPN
ap-7354	232	5	)	)	PUNCT
ap-7354	232	6	,	,	PUNCT
ap-7354	232	7	(	(	PUNCT
ap-7354	232	8	58	58	NUM
ap-7354	232	9	)	)	PUNCT
ap-7354	232	10	where	where	SCONJ
ap-7354	232	11	[	[	PUNCT
ap-7354	232	12	bj	bj	NOUN
ap-7354	232	13	,	,	PUNCT
ap-7354	232	14	b	b	PROPN
ap-7354	232	15	†	†	X
ap-7354	232	16	j	j	PROPN
ap-7354	232	17	]	]	X
ap-7354	233	1	=	=	PUNCT
ap-7354	233	2	1	1	NUM
ap-7354	233	3	,	,	PUNCT
ap-7354	233	4	with	with	ADP
ap-7354	233	5	b†	b†	PROPN
ap-7354	233	6	jbj	jbj	PROPN
ap-7354	233	7	=	=	PROPN
ap-7354	233	8	nj	nj	PROPN
ap-7354	233	9	.	.	PUNCT
ap-7354	234	1	(	(	PUNCT
ap-7354	234	2	59	59	NUM
ap-7354	234	3	)	)	PUNCT
ap-7354	234	4	the	the	DET
ap-7354	234	5	above	above	ADJ
ap-7354	234	6	creation	creation	NOUN
ap-7354	234	7	and	and	CCONJ
ap-7354	234	8	annihilation	annihilation	NOUN
ap-7354	234	9	operators	operator	NOUN
ap-7354	234	10	are	be	AUX
ap-7354	234	11	,	,	PUNCT
ap-7354	234	12	in	in	ADP
ap-7354	234	13	fact	fact	NOUN
ap-7354	234	14	,	,	PUNCT
ap-7354	234	15	extracted	extract	VERB
ap-7354	234	16	from	from	ADP
ap-7354	234	17	the	the	DET
ap-7354	234	18	one	one	NUM
ap-7354	234	19	in	in	ADP
ap-7354	234	20	3.2	3.2	NUM
ap-7354	234	21	,	,	PUNCT
ap-7354	234	22	when	when	SCONJ
ap-7354	234	23	(	(	PUNCT
ap-7354	234	24	a	a	DET
ap-7354	234	25	,	,	PUNCT
ap-7354	234	26	a†	a†	NOUN
ap-7354	234	27	)	)	PUNCT
ap-7354	234	28	=	=	NOUN
ap-7354	234	29	{	{	PUNCT
ap-7354	234	30	i	i	PRON
ap-7354	234	31	(	(	PUNCT
ap-7354	234	32	ax	ax	NOUN
ap-7354	234	33	+	+	CCONJ
ap-7354	234	34	iay	iay	NOUN
ap-7354	234	35	)	)	PUNCT
ap-7354	234	36	,	,	PUNCT
ap-7354	234	37	−i	−i	PROPN
ap-7354	234	38	(	(	PUNCT
ap-7354	234	39	a†	a†	X
ap-7354	234	40	x	x	SYM
ap-7354	234	41	−	−	PROPN
ap-7354	234	42	ia†	ia†	PROPN
ap-7354	234	43	y	y	NOUN
ap-7354	234	44	)	)	PUNCT
ap-7354	234	45	}	}	PUNCT
ap-7354	234	46	|θ→0→	|θ→0→	VERB
ap-7354	234	47	(	(	PUNCT
ap-7354	234	48	b	b	NOUN
ap-7354	234	49	,	,	PUNCT
ap-7354	234	50	b†	b†	ADJ
ap-7354	234	51	)	)	PUNCT
ap-7354	234	52	=	=	PRON
ap-7354	234	53	{	{	PUNCT
ap-7354	234	54	i	i	PRON
ap-7354	234	55	(	(	PUNCT
ap-7354	234	56	bx	bx	PROPN
ap-7354	234	57	+	+	CCONJ
ap-7354	234	58	iby	iby	PROPN
ap-7354	234	59	)	)	PUNCT
ap-7354	234	60	,	,	PUNCT
ap-7354	234	61	−i	−i	PROPN
ap-7354	234	62	(	(	PUNCT
ap-7354	234	63	b†	b†	PROPN
ap-7354	234	64	x	x	SYM
ap-7354	234	65	−	−	PROPN
ap-7354	234	66	ib†	ib†	ADP
ap-7354	234	67	y	y	PROPN
ap-7354	234	68	)	)	PUNCT
ap-7354	234	69	}	}	PUNCT
ap-7354	234	70	(	(	PUNCT
ap-7354	234	71	because	because	SCONJ
ap-7354	234	72	in	in	ADP
ap-7354	234	73	3.3	3.3	NUM
ap-7354	234	74	,	,	PUNCT
ap-7354	234	75	we	we	PRON
ap-7354	234	76	deal	deal	VERB
ap-7354	234	77	only	only	ADV
ap-7354	234	78	with	with	ADP
ap-7354	234	79	τ	τ	PROPN
ap-7354	234	80	)	)	PUNCT
ap-7354	234	81	.	.	PUNCT
ap-7354	235	1	in	in	ADP
ap-7354	235	2	fact	fact	NOUN
ap-7354	235	3	,	,	PUNCT
ap-7354	235	4	we	we	PRON
ap-7354	235	5	have	have	VERB
ap-7354	235	6	only	only	ADV
ap-7354	235	7	one	one	NUM
ap-7354	235	8	integer	integer	NOUN
ap-7354	235	9	,	,	PUNCT
ap-7354	235	10	which	which	PRON
ap-7354	235	11	is	be	AUX
ap-7354	235	12	n	n	CCONJ
ap-7354	235	13	,	,	PUNCT
ap-7354	235	14	but	but	CCONJ
ap-7354	235	15	with	with	ADP
ap-7354	235	16	the	the	DET
ap-7354	235	17	feature	feature	NOUN
ap-7354	235	18	n	n	NOUN
ap-7354	235	19	=	=	SYM
ap-7354	235	20	nx	nx	PROPN
ap-7354	235	21	+	+	CCONJ
ap-7354	235	22	ny	ny	PROPN
ap-7354	235	23	.	.	PUNCT
ap-7354	236	1	we	we	PRON
ap-7354	236	2	deliberately	deliberately	ADV
ap-7354	236	3	use	use	VERB
ap-7354	236	4	nx	nx	PROPN
ap-7354	236	5	,	,	PUNCT
ap-7354	236	6	ny	ny	PROPN
ap-7354	236	7	instead	instead	ADV
ap-7354	236	8	of	of	ADP
ap-7354	236	9	n	n	PRON
ap-7354	236	10	because	because	SCONJ
ap-7354	236	11	in	in	ADP
ap-7354	236	12	the	the	DET
ap-7354	236	13	perturbed	perturb	VERB
ap-7354	236	14	hamiltonian	hamiltonian	NOUN
ap-7354	236	15	,	,	PUNCT
ap-7354	236	16	we	we	PRON
ap-7354	236	17	can	can	AUX
ap-7354	236	18	not	not	PART
ap-7354	236	19	use	use	VERB
ap-7354	236	20	a	a	DET
ap-7354	236	21	complex	complex	ADJ
ap-7354	236	22	formalism	formalism	NOUN
ap-7354	236	23	,	,	PUNCT
ap-7354	236	24	thus	thus	ADV
ap-7354	236	25	we	we	PRON
ap-7354	236	26	divide	divide	VERB
ap-7354	236	27	n	n	X
ap-7354	236	28	into	into	ADP
ap-7354	236	29	nx	nx	PROPN
ap-7354	236	30	and	and	CCONJ
ap-7354	236	31	ny	ny	PROPN
ap-7354	236	32	.	.	PROPN
ap-7354	237	1	with	with	ADP
ap-7354	237	2	the	the	DET
ap-7354	237	3	help	help	NOUN
ap-7354	237	4	of	of	ADP
ap-7354	237	5	the	the	DET
ap-7354	237	6	following	follow	VERB
ap-7354	237	7	definitions	definition	NOUN
ap-7354	237	8	of	of	ADP
ap-7354	237	9	eigenkets	eigenket	NOUN
ap-7354	237	10	and	and	CCONJ
ap-7354	237	11	central	central	ADJ
ap-7354	237	12	properties	property	NOUN
ap-7354	237	13	of	of	ADP
ap-7354	237	14	creation	creation	NOUN
ap-7354	237	15	and	and	CCONJ
ap-7354	237	16	annihilation	annihilation	NOUN
ap-7354	237	17	operators	operator	NOUN
ap-7354	237	18	[	[	X
ap-7354	237	19	35	35	NUM
ap-7354	237	20	]	]	SYM
ap-7354	237	21	bj	bj	NOUN
ap-7354	237	22	|	|	ADV
ap-7354	237	23	nj	nj	INTJ
ap-7354	237	24	>	>	PUNCT
ap-7354	238	1	=	=	PUNCT
ap-7354	239	1	√	√	PROPN
ap-7354	239	2	nj	nj	PROPN
ap-7354	240	1	|	|	INTJ
ap-7354	240	2	nj	nj	PROPN
ap-7354	241	1	−	−	NOUN
ap-7354	241	2	1	1	NUM
ap-7354	241	3	>	>	PUNCT
ap-7354	241	4	,	,	PUNCT
ap-7354	241	5	b†	b†	PROPN
ap-7354	241	6	j	j	PROPN
ap-7354	242	1	|	|	ADV
ap-7354	242	2	nj	nj	INTJ
ap-7354	242	3	>	>	PUNCT
ap-7354	243	1	=	=	PUNCT
ap-7354	244	1	√	√	NUM
ap-7354	244	2	nj	nj	NOUN
ap-7354	245	1	+	+	CCONJ
ap-7354	245	2	1	1	NUM
ap-7354	245	3	|	|	ADV
ap-7354	245	4	nj	nj	PROPN
ap-7354	246	1	+	+	CCONJ
ap-7354	246	2	1	1	NUM
ap-7354	246	3	>	>	PUNCT
ap-7354	246	4	,	,	PUNCT
ap-7354	246	5	b2	b2	NOUN
ap-7354	246	6	j	j	NOUN
ap-7354	246	7	|	|	ADV
ap-7354	246	8	nj	nj	INTJ
ap-7354	246	9	>	>	PUNCT
ap-7354	247	1	=	=	PUNCT
ap-7354	247	2	√	√	NUM
ap-7354	247	3	nj	nj	PROPN
ap-7354	247	4	(	(	PUNCT
ap-7354	247	5	nj	nj	PROPN
ap-7354	247	6	−	−	PROPN
ap-7354	247	7	1	1	X
ap-7354	247	8	)	)	PUNCT
ap-7354	248	1	|	|	ADV
ap-7354	248	2	nj	nj	INTJ
ap-7354	249	1	−	−	NOUN
ap-7354	249	2	2	2	NUM
ap-7354	249	3	>	>	PUNCT
ap-7354	249	4	,	,	PUNCT
ap-7354	249	5	b†2	b†2	ADP
ap-7354	249	6	j	j	PROPN
ap-7354	249	7	|	|	ADV
ap-7354	249	8	nj	nj	INTJ
ap-7354	249	9	>	>	PUNCT
ap-7354	249	10	=	=	PUNCT
ap-7354	250	1	√	√	NUM
ap-7354	250	2	(	(	PUNCT
ap-7354	250	3	nj	nj	PROPN
ap-7354	250	4	+	+	CCONJ
ap-7354	250	5	1	1	X
ap-7354	250	6	)	)	PUNCT
ap-7354	250	7	(	(	PUNCT
ap-7354	250	8	nj	nj	PROPN
ap-7354	250	9	+	+	CCONJ
ap-7354	250	10	2	2	X
ap-7354	250	11	)	)	PUNCT
ap-7354	251	1	|	|	ADV
ap-7354	251	2	nj	nj	PROPN
ap-7354	252	1	+	+	CCONJ
ap-7354	252	2	2	2	NUM
ap-7354	252	3	>	>	PUNCT
ap-7354	252	4	,	,	PUNCT
ap-7354	252	5	b3	b3	PROPN
ap-7354	252	6	j	j	PROPN
ap-7354	252	7	|	|	ADV
ap-7354	252	8	nj	nj	INTJ
ap-7354	252	9	>	>	PUNCT
ap-7354	253	1	=	=	PUNCT
ap-7354	253	2	√	√	NUM
ap-7354	253	3	nj	nj	PROPN
ap-7354	253	4	(	(	PUNCT
ap-7354	253	5	nj	nj	PROPN
ap-7354	253	6	−	−	PROPN
ap-7354	253	7	1	1	NUM
ap-7354	253	8	)	)	PUNCT
ap-7354	253	9	(	(	PUNCT
ap-7354	253	10	nj	nj	NOUN
ap-7354	253	11	−	−	NOUN
ap-7354	253	12	2	2	X
ap-7354	253	13	)	)	PUNCT
ap-7354	254	1	|	|	ADV
ap-7354	254	2	nj	nj	INTJ
ap-7354	255	1	−	−	NOUN
ap-7354	255	2	3	3	NUM
ap-7354	255	3	>	>	PUNCT
ap-7354	255	4	,	,	PUNCT
ap-7354	255	5	b†3	b†3	PROPN
ap-7354	255	6	j	j	PROPN
ap-7354	256	1	|	|	ADV
ap-7354	256	2	nj	nj	INTJ
ap-7354	256	3	>	>	PUNCT
ap-7354	257	1	=	=	PUNCT
ap-7354	257	2	√	√	NUM
ap-7354	257	3	(	(	PUNCT
ap-7354	257	4	nj	nj	PROPN
ap-7354	257	5	+	+	CCONJ
ap-7354	257	6	1	1	X
ap-7354	257	7	)	)	PUNCT
ap-7354	257	8	(	(	PUNCT
ap-7354	257	9	nj	nj	PROPN
ap-7354	257	10	+	+	CCONJ
ap-7354	257	11	2	2	X
ap-7354	257	12	)	)	PUNCT
ap-7354	257	13	(	(	PUNCT
ap-7354	257	14	nj	nj	PROPN
ap-7354	257	15	+	+	CCONJ
ap-7354	257	16	3	3	X
ap-7354	257	17	)	)	PUNCT
ap-7354	258	1	|	|	ADV
ap-7354	258	2	nj	nj	PROPN
ap-7354	259	1	+	+	CCONJ
ap-7354	259	2	3	3	NUM
ap-7354	259	3	>	>	PUNCT
ap-7354	259	4	,	,	PUNCT
ap-7354	259	5	...	...	PUNCT
ap-7354	259	6	(	(	PUNCT
ap-7354	259	7	60	60	NUM
ap-7354	259	8	)	)	PUNCT
ap-7354	259	9	697	697	NUM
ap-7354	259	10	ilyas	ilyas	NOUN
ap-7354	259	11	haouam	haouam	VERB
ap-7354	259	12	acta	acta	PROPN
ap-7354	259	13	polytechnica	polytechnica	PROPN
ap-7354	259	14	with	with	ADP
ap-7354	259	15	<	<	X
ap-7354	259	16	n	n	CCONJ
ap-7354	260	1	′	′	NUM
ap-7354	260	2	j	j	PROPN
ap-7354	261	1	|	|	ADV
ap-7354	261	2	nj	nj	INTJ
ap-7354	261	3	>	>	PUNCT
ap-7354	261	4	=	=	PUNCT
ap-7354	262	1	δn	δn	ADJ
ap-7354	262	2	′	′	NUM
ap-7354	262	3	j	j	PROPN
ap-7354	262	4	,	,	PUNCT
ap-7354	262	5	nj	nj	PROPN
ap-7354	262	6	and	and	CCONJ
ap-7354	262	7	[	[	PUNCT
ap-7354	262	8	b†b	b†b	NUM
ap-7354	262	9	,	,	PUNCT
ap-7354	262	10	b†	b†	ADJ
ap-7354	262	11	]	]	PUNCT
ap-7354	262	12	=	=	SYM
ap-7354	262	13	b†bb†	b†bb†	NOUN
ap-7354	262	14	−	−	NOUN
ap-7354	262	15	b†2b	b†2b	NOUN
ap-7354	262	16	=	=	SYM
ap-7354	262	17	b†	b†	PROPN
ap-7354	262	18	and	and	CCONJ
ap-7354	262	19	[	[	PUNCT
ap-7354	262	20	b†b	b†b	NUM
ap-7354	262	21	,	,	PUNCT
ap-7354	262	22	b	b	NOUN
ap-7354	262	23	]	]	X
ap-7354	262	24	=	=	SYM
ap-7354	262	25	b†b2	b†b2	PROPN
ap-7354	262	26	−	−	PROPN
ap-7354	262	27	bb†b	bb†b	NOUN
ap-7354	262	28	=	=	PUNCT
ap-7354	262	29	−b	−b	NOUN
ap-7354	262	30	,	,	PUNCT
ap-7354	262	31	(	(	PUNCT
ap-7354	262	32	61	61	NUM
ap-7354	262	33	)	)	PUNCT
ap-7354	262	34	b†bb†	b†bb†	NOUN
ap-7354	263	1	|	|	ADV
ap-7354	263	2	n	n	NOUN
ap-7354	263	3	>	>	PUNCT
ap-7354	263	4	=	=	PUNCT
ap-7354	264	1	nb†	nb†	PROPN
ap-7354	264	2	|	|	ADV
ap-7354	264	3	n	n	NOUN
ap-7354	264	4	>	>	PUNCT
ap-7354	264	5	=	=	SYM
ap-7354	264	6	(	(	PUNCT
ap-7354	264	7	n+	n+	NOUN
ap-7354	264	8	1	1	NUM
ap-7354	264	9	)	)	PUNCT
ap-7354	264	10	b†	b†	ADJ
ap-7354	265	1	|	|	ADV
ap-7354	265	2	n	n	CCONJ
ap-7354	265	3	>	>	PUNCT
ap-7354	265	4	,	,	PUNCT
ap-7354	265	5	(	(	PUNCT
ap-7354	265	6	62	62	NUM
ap-7354	265	7	)	)	PUNCT
ap-7354	266	1	b†bb	b†bb	PROPN
ap-7354	266	2	|	|	ADV
ap-7354	266	3	n	n	NOUN
ap-7354	266	4	>	>	PUNCT
ap-7354	267	1	=	=	SYM
ap-7354	267	2	nb	nb	PROPN
ap-7354	268	1	|	|	ADV
ap-7354	268	2	n	n	CCONJ
ap-7354	268	3	>	>	PUNCT
ap-7354	268	4	=	=	PUNCT
ap-7354	268	5	(	(	PUNCT
ap-7354	268	6	n−	n−	NOUN
ap-7354	268	7	1	1	NUM
ap-7354	268	8	)	)	PUNCT
ap-7354	268	9	b	b	NOUN
ap-7354	269	1	|	|	ADV
ap-7354	269	2	n	n	CCONJ
ap-7354	269	3	>	>	X
ap-7354	269	4	,	,	PUNCT
ap-7354	269	5	(	(	PUNCT
ap-7354	269	6	63	63	NUM
ap-7354	269	7	)	)	PUNCT
ap-7354	270	1	[	[	X
ap-7354	270	2	n	n	CCONJ
ap-7354	270	3	,	,	PUNCT
ap-7354	270	4	b	b	X
ap-7354	270	5	]	]	X
ap-7354	270	6	=	=	SYM
ap-7354	270	7	−b	−b	NOUN
ap-7354	270	8	and	and	CCONJ
ap-7354	270	9	bn	bn	NOUN
ap-7354	270	10	=	=	PUNCT
ap-7354	270	11	nb+	nb+	PROPN
ap-7354	270	12	b	b	NOUN
ap-7354	270	13	,	,	PUNCT
ap-7354	270	14	(	(	PUNCT
ap-7354	270	15	64	64	NUM
ap-7354	270	16	)	)	PUNCT
ap-7354	270	17	[	[	PUNCT
ap-7354	270	18	n	n	CCONJ
ap-7354	270	19	,	,	PUNCT
ap-7354	270	20	b†	b†	PROPN
ap-7354	270	21	]	]	PUNCT
ap-7354	270	22	=	=	SYM
ap-7354	270	23	b†	b†	ADJ
ap-7354	270	24	and	and	CCONJ
ap-7354	270	25	b†n	b†n	NUM
ap-7354	270	26	=	=	SYM
ap-7354	270	27	nb†	nb†	PROPN
ap-7354	271	1	−	−	PROPN
ap-7354	271	2	b†.	b†.	NOUN
ap-7354	271	3	(	(	PUNCT
ap-7354	271	4	65	65	NUM
ap-7354	271	5	)	)	PUNCT
ap-7354	271	6	knowing	know	VERB
ap-7354	271	7	that	that	SCONJ
ap-7354	271	8	xs	xs	PROPN
ap-7354	271	9	j	j	PROPN
ap-7354	271	10	=	=	PUNCT
ap-7354	271	11	√	√	PROPN
ap-7354	271	12	ℏ	ℏ	PROPN
ap-7354	271	13	2mω	2mω	NOUN
ap-7354	271	14	(	(	PUNCT
ap-7354	271	15	bj	bj	X
ap-7354	271	16	+	+	CCONJ
ap-7354	271	17	b†	b†	ADJ
ap-7354	271	18	j	j	PROPN
ap-7354	271	19	)	)	PUNCT
ap-7354	271	20	and	and	CCONJ
ap-7354	271	21	ps	ps	PROPN
ap-7354	271	22	j	j	PROPN
ap-7354	271	23	=	=	PRON
ap-7354	272	1	i	i	PRON
ap-7354	272	2	√	√	VERB
ap-7354	272	3	ℏmω	ℏmω	NOUN
ap-7354	272	4	2	2	NUM
ap-7354	272	5	(	(	PUNCT
ap-7354	272	6	b†	b†	ADJ
ap-7354	272	7	j	j	NOUN
ap-7354	272	8	−	−	NOUN
ap-7354	272	9	bj	bj	NOUN
ap-7354	272	10	)	)	PUNCT
ap-7354	272	11	.	.	PUNCT
ap-7354	273	1	(	(	PUNCT
ap-7354	273	2	66	66	NUM
ap-7354	273	3	)	)	PUNCT
ap-7354	273	4	the	the	DET
ap-7354	273	5	contributions	contribution	NOUN
ap-7354	273	6	of	of	ADP
ap-7354	273	7	the	the	DET
ap-7354	273	8	different	different	ADJ
ap-7354	273	9	parts	part	NOUN
ap-7354	273	10	of	of	ADP
ap-7354	273	11	the	the	DET
ap-7354	273	12	perturbed	perturb	VERB
ap-7354	273	13	hamiltonian	hamiltonian	NOUN
ap-7354	273	14	are	be	AUX
ap-7354	273	15	as	as	SCONJ
ap-7354	273	16	follows	follow	VERB
ap-7354	273	17	<	<	X
ap-7354	273	18	nx	nx	PROPN
ap-7354	273	19	,	,	PUNCT
ap-7354	273	20	ny	ny	PROPN
ap-7354	273	21	|	|	ADV
ap-7354	273	22	v1	v1	NOUN
ap-7354	274	1	|	|	ADV
ap-7354	274	2	n	n	NOUN
ap-7354	274	3	′	′	NUM
ap-7354	274	4	x	x	NOUN
ap-7354	274	5	,	,	PUNCT
ap-7354	274	6	n	n	PROPN
ap-7354	274	7	′	′	NOUN
ap-7354	274	8	y	y	NOUN
ap-7354	274	9	>	>	PUNCT
ap-7354	274	10	=	=	X
ap-7354	274	11	<	<	X
ap-7354	274	12	nx	nx	PROPN
ap-7354	274	13	,	,	PUNCT
ap-7354	274	14	ny	ny	PROPN
ap-7354	275	1	|	|	ADV
ap-7354	275	2	(	(	PUNCT
ap-7354	275	3	ys)2	ys)2	NOUN
ap-7354	275	4	ps	ps	PROPN
ap-7354	275	5	y	y	PROPN
ap-7354	275	6	|	|	ADV
ap-7354	275	7	n	n	ADV
ap-7354	276	1	′	′	NUM
ap-7354	276	2	x	x	NOUN
ap-7354	276	3	,	,	PUNCT
ap-7354	276	4	n	n	PROPN
ap-7354	276	5	′	′	NOUN
ap-7354	277	1	y	y	NOUN
ap-7354	277	2	>	>	PUNCT
ap-7354	277	3	=	=	PUNCT
ap-7354	277	4	−iℏ	−iℏ	PROPN
ap-7354	277	5	2	2	NUM
ap-7354	277	6	√	√	PROPN
ap-7354	277	7	ℏ	ℏ	PROPN
ap-7354	277	8	2mωδnx	2mωδnx	NUM
ap-7354	277	9	,	,	PUNCT
ap-7354	277	10	n′	n′	NOUN
ap-7354	277	11	x	x	X
ap-7354	277	12	{	{	PUNCT
ap-7354	277	13	√	√	INTJ
ap-7354	277	14	n′	n′	PROPN
ap-7354	277	15	y	y	PROPN
ap-7354	277	16	(	(	PUNCT
ap-7354	277	17	n′	n′	NOUN
ap-7354	277	18	y	y	PROPN
ap-7354	277	19	−	−	PROPN
ap-7354	277	20	1	1	NUM
ap-7354	277	21	)	)	PUNCT
ap-7354	277	22	(	(	PUNCT
ap-7354	277	23	n′	n′	NOUN
ap-7354	277	24	y	y	PROPN
ap-7354	277	25	−	−	PROPN
ap-7354	277	26	2	2	NUM
ap-7354	277	27	)	)	PUNCT
ap-7354	277	28	δny	δny	NOUN
ap-7354	277	29	,	,	PUNCT
ap-7354	277	30	n′	n′	PROPN
ap-7354	277	31	y−3	y−3	PROPN
ap-7354	277	32	−	−	PROPN
ap-7354	277	33	√	√	PROPN
ap-7354	277	34	(	(	PUNCT
ap-7354	277	35	n′	n′	NOUN
ap-7354	277	36	y	y	PROPN
ap-7354	277	37	+	+	NOUN
ap-7354	277	38	1	1	NUM
ap-7354	277	39	)	)	PUNCT
ap-7354	277	40	(	(	PUNCT
ap-7354	277	41	n′	n′	NOUN
ap-7354	277	42	y	y	PROPN
ap-7354	278	1	+	+	CCONJ
ap-7354	278	2	2	2	NUM
ap-7354	278	3	)	)	PUNCT
ap-7354	278	4	(	(	PUNCT
ap-7354	278	5	n′	n′	NOUN
ap-7354	278	6	y	y	PROPN
ap-7354	278	7	+	+	CCONJ
ap-7354	278	8	3	3	X
ap-7354	278	9	)	)	PUNCT
ap-7354	278	10	δny	δny	NOUN
ap-7354	278	11	,	,	PUNCT
ap-7354	278	12	n′	n′	NOUN
ap-7354	278	13	y+3	y+3	NOUN
ap-7354	279	1	+	+	CCONJ
ap-7354	279	2	(	(	PUNCT
ap-7354	279	3	n	n	ADV
ap-7354	279	4	′	′	NUM
ap-7354	279	5	y	y	NOUN
ap-7354	280	1	−	−	PROPN
ap-7354	280	2	2	2	NUM
ap-7354	280	3	)	)	PUNCT
ap-7354	280	4	√	√	PROPN
ap-7354	280	5	n′	n′	PRON
ap-7354	280	6	yδny	yδny	NOUN
ap-7354	280	7	,	,	PUNCT
ap-7354	280	8	n′	n′	PROPN
ap-7354	280	9	y−1	y−1	PROPN
ap-7354	280	10	−	−	PROPN
ap-7354	281	1	(	(	PUNCT
ap-7354	281	2	n	n	NOUN
ap-7354	281	3	′	′	NUM
ap-7354	281	4	y	y	NOUN
ap-7354	282	1	+	+	CCONJ
ap-7354	282	2	3	3	NUM
ap-7354	282	3	)	)	PUNCT
ap-7354	282	4	√	√	PROPN
ap-7354	282	5	n′	n′	PROPN
ap-7354	282	6	y	y	PROPN
ap-7354	282	7	+	+	NUM
ap-7354	282	8	1δny	1δny	NUM
ap-7354	282	9	,	,	PUNCT
ap-7354	282	10	n′	n′	NOUN
ap-7354	282	11	y+1	y+1	NUM
ap-7354	282	12	}	}	PUNCT
ap-7354	282	13	.	.	PUNCT
ap-7354	283	1	(	(	PUNCT
ap-7354	283	2	67	67	NUM
ap-7354	283	3	)	)	PUNCT
ap-7354	283	4	<	<	X
ap-7354	283	5	nx	nx	PROPN
ap-7354	283	6	,	,	PUNCT
ap-7354	283	7	ny	ny	PROPN
ap-7354	284	1	|	|	ADV
ap-7354	284	2	v2	v2	INTJ
ap-7354	285	1	|	|	ADV
ap-7354	285	2	n	n	NOUN
ap-7354	285	3	′	′	NUM
ap-7354	286	1	x	x	NOUN
ap-7354	286	2	,	,	PUNCT
ap-7354	286	3	n	n	PROPN
ap-7354	286	4	′	′	NOUN
ap-7354	287	1	y	y	NOUN
ap-7354	287	2	>	>	PUNCT
ap-7354	287	3	=	=	X
ap-7354	287	4	<	<	X
ap-7354	287	5	nx	nx	PROPN
ap-7354	287	6	,	,	PUNCT
ap-7354	287	7	ny	ny	PROPN
ap-7354	288	1	|	|	ADV
ap-7354	288	2	ps	ps	PROPN
ap-7354	288	3	y	y	PROPN
ap-7354	288	4	(	(	PUNCT
ap-7354	288	5	ys)2	ys)2	NOUN
ap-7354	289	1	|	|	ADV
ap-7354	289	2	n	n	NOUN
ap-7354	289	3	′	′	NUM
ap-7354	290	1	x	x	NOUN
ap-7354	290	2	,	,	PUNCT
ap-7354	290	3	n	n	PROPN
ap-7354	290	4	′	′	NOUN
ap-7354	290	5	y	y	NOUN
ap-7354	290	6	>	>	PUNCT
ap-7354	290	7	=	=	PUNCT
ap-7354	290	8	−iℏ	−iℏ	PROPN
ap-7354	290	9	2	2	NUM
ap-7354	290	10	√	√	PROPN
ap-7354	290	11	ℏ	ℏ	PROPN
ap-7354	290	12	2mωδnx	2mωδnx	NUM
ap-7354	290	13	,	,	PUNCT
ap-7354	290	14	n′	n′	NOUN
ap-7354	290	15	x	x	X
ap-7354	290	16	{	{	PUNCT
ap-7354	290	17	√	√	INTJ
ap-7354	290	18	n′	n′	PROPN
ap-7354	290	19	y	y	PROPN
ap-7354	290	20	(	(	PUNCT
ap-7354	290	21	n′	n′	NOUN
ap-7354	290	22	y	y	PROPN
ap-7354	290	23	−	−	PROPN
ap-7354	290	24	1	1	NUM
ap-7354	290	25	)	)	PUNCT
ap-7354	290	26	(	(	PUNCT
ap-7354	290	27	n′	n′	NOUN
ap-7354	290	28	y	y	PROPN
ap-7354	290	29	−	−	PROPN
ap-7354	290	30	2	2	NUM
ap-7354	290	31	)	)	PUNCT
ap-7354	290	32	δny	δny	NOUN
ap-7354	290	33	,	,	PUNCT
ap-7354	290	34	n′	n′	PROPN
ap-7354	290	35	y−3	y−3	PROPN
ap-7354	290	36	−	−	PROPN
ap-7354	290	37	√	√	PROPN
ap-7354	290	38	(	(	PUNCT
ap-7354	290	39	n′	n′	NOUN
ap-7354	290	40	y	y	PROPN
ap-7354	290	41	+	+	NOUN
ap-7354	290	42	1	1	NUM
ap-7354	290	43	)	)	PUNCT
ap-7354	290	44	(	(	PUNCT
ap-7354	290	45	n′	n′	NOUN
ap-7354	290	46	y	y	PROPN
ap-7354	291	1	+	+	CCONJ
ap-7354	291	2	2	2	NUM
ap-7354	291	3	)	)	PUNCT
ap-7354	291	4	(	(	PUNCT
ap-7354	291	5	n′	n′	NOUN
ap-7354	291	6	y	y	PROPN
ap-7354	291	7	+	+	CCONJ
ap-7354	291	8	3	3	X
ap-7354	291	9	)	)	PUNCT
ap-7354	291	10	δny	δny	NOUN
ap-7354	291	11	,	,	PUNCT
ap-7354	291	12	n′	n′	NOUN
ap-7354	291	13	y+3	y+3	NOUN
ap-7354	292	1	+	+	CCONJ
ap-7354	292	2	(	(	PUNCT
ap-7354	292	3	n	n	ADV
ap-7354	292	4	′	′	NUM
ap-7354	292	5	y	y	NOUN
ap-7354	292	6	+	+	CCONJ
ap-7354	292	7	2	2	NUM
ap-7354	292	8	)	)	PUNCT
ap-7354	292	9	√	√	PROPN
ap-7354	292	10	n′	n′	PRON
ap-7354	292	11	yδny	yδny	NOUN
ap-7354	292	12	,	,	PUNCT
ap-7354	292	13	n′	n′	PROPN
ap-7354	292	14	y−1	y−1	PROPN
ap-7354	293	1	+	+	CCONJ
ap-7354	293	2	(	(	PUNCT
ap-7354	293	3	3	3	NUM
ap-7354	293	4	−	−	NOUN
ap-7354	293	5	n	n	NOUN
ap-7354	293	6	′	′	NOUN
ap-7354	293	7	y	y	PROPN
ap-7354	293	8	)	)	PUNCT
ap-7354	294	1	√	√	PROPN
ap-7354	294	2	n′	n′	PROPN
ap-7354	294	3	y	y	PROPN
ap-7354	294	4	+	+	NUM
ap-7354	294	5	1δny	1δny	NUM
ap-7354	294	6	,	,	PUNCT
ap-7354	294	7	n′	n′	NOUN
ap-7354	294	8	y+1	y+1	NUM
ap-7354	294	9	}	}	PUNCT
ap-7354	294	10	.	.	PUNCT
ap-7354	295	1	(	(	PUNCT
ap-7354	295	2	68	68	NUM
ap-7354	295	3	)	)	PUNCT
ap-7354	295	4	<	<	X
ap-7354	295	5	nx	nx	PROPN
ap-7354	295	6	,	,	PUNCT
ap-7354	295	7	ny	ny	PROPN
ap-7354	295	8	|	|	PROPN
ap-7354	295	9	v3	v3	PROPN
ap-7354	295	10	|	|	ADV
ap-7354	295	11	n	n	NOUN
ap-7354	296	1	′	′	NUM
ap-7354	296	2	x	x	NOUN
ap-7354	296	3	,	,	PUNCT
ap-7354	296	4	n	n	PROPN
ap-7354	296	5	′	′	NOUN
ap-7354	297	1	y	y	NOUN
ap-7354	297	2	>	>	PUNCT
ap-7354	297	3	=	=	X
ap-7354	297	4	<	<	X
ap-7354	297	5	nx	nx	PROPN
ap-7354	297	6	,	,	PUNCT
ap-7354	297	7	ny	ny	PROPN
ap-7354	298	1	|	|	ADV
ap-7354	298	2	xs	xs	PROPN
ap-7354	299	1	(	(	PUNCT
ap-7354	299	2	ys)2	ys)2	NOUN
ap-7354	299	3	|	|	ADV
ap-7354	299	4	n	n	NOUN
ap-7354	299	5	′	′	NUM
ap-7354	299	6	x	x	NOUN
ap-7354	299	7	,	,	PUNCT
ap-7354	299	8	n	n	PROPN
ap-7354	299	9	′	′	NOUN
ap-7354	300	1	y	y	NOUN
ap-7354	300	2	>	>	PUNCT
ap-7354	300	3	=	=	PUNCT
ap-7354	301	1	(	(	PUNCT
ap-7354	301	2	ℏ	ℏ	PROPN
ap-7354	301	3	2mω	2mω	NOUN
ap-7354	301	4	)	)	PUNCT
ap-7354	301	5	3	3	NUM
ap-7354	301	6	2	2	NUM
ap-7354	301	7	(	(	PUNCT
ap-7354	301	8	√	√	PROPN
ap-7354	301	9	n′	n′	PROPN
ap-7354	301	10	xδnx	xδnx	PROPN
ap-7354	301	11	,	,	PUNCT
ap-7354	301	12	n′	n′	PROPN
ap-7354	301	13	x−1	x−1	PROPN
ap-7354	302	1	+	+	CCONJ
ap-7354	302	2	√	√	VERB
ap-7354	302	3	n′	n′	NOUN
ap-7354	302	4	x	x	PUNCT
ap-7354	303	1	+	+	NUM
ap-7354	303	2	1δnx	1δnx	NUM
ap-7354	303	3	,	,	PUNCT
ap-7354	303	4	n′	n′	PROPN
ap-7354	303	5	x+1	x+1	NUM
ap-7354	303	6	)	)	PUNCT
ap-7354	304	1	×	×	NOUN
ap-7354	304	2	(	(	PUNCT
ap-7354	304	3	√	√	PROPN
ap-7354	304	4	n′	n′	PROPN
ap-7354	304	5	y	y	PROPN
ap-7354	304	6	(	(	PUNCT
ap-7354	304	7	n′	n′	NOUN
ap-7354	304	8	y	y	PROPN
ap-7354	304	9	−	−	PROPN
ap-7354	304	10	1	1	NUM
ap-7354	304	11	)	)	PUNCT
ap-7354	304	12	δny	δny	NOUN
ap-7354	304	13	,	,	PUNCT
ap-7354	304	14	n′	n′	NOUN
ap-7354	305	1	y−2	y−2	PROPN
ap-7354	306	1	+	+	CCONJ
ap-7354	306	2	√	√	PROPN
ap-7354	306	3	(	(	PUNCT
ap-7354	306	4	n′	n′	NOUN
ap-7354	306	5	y	y	PROPN
ap-7354	306	6	+	+	NOUN
ap-7354	306	7	1	1	NUM
ap-7354	306	8	)	)	PUNCT
ap-7354	306	9	(	(	PUNCT
ap-7354	306	10	n′	n′	NOUN
ap-7354	306	11	y	y	PROPN
ap-7354	306	12	+	+	CCONJ
ap-7354	306	13	2	2	X
ap-7354	306	14	)	)	PUNCT
ap-7354	306	15	δny	δny	NOUN
ap-7354	306	16	,	,	PUNCT
ap-7354	306	17	n′	n′	NOUN
ap-7354	306	18	y+2	y+2	PROPN
ap-7354	306	19	+	+	CCONJ
ap-7354	306	20	(	(	PUNCT
ap-7354	306	21	1	1	NUM
ap-7354	306	22	+	+	NUM
ap-7354	306	23	2n	2n	NUM
ap-7354	306	24	′	′	NUM
ap-7354	306	25	y	y	NOUN
ap-7354	306	26	)	)	PUNCT
ap-7354	306	27	δny	δny	PROPN
ap-7354	306	28	,	,	PUNCT
ap-7354	306	29	n′	n′	PROPN
ap-7354	306	30	y	y	PROPN
ap-7354	306	31	)	)	PUNCT
ap-7354	306	32	.	.	PUNCT
ap-7354	307	1	(	(	PUNCT
ap-7354	307	2	69	69	NUM
ap-7354	307	3	)	)	PUNCT
ap-7354	307	4	the	the	DET
ap-7354	307	5	relevant	relevant	ADJ
ap-7354	307	6	perturbation	perturbation	NOUN
ap-7354	307	7	matrix	matrix	NOUN
ap-7354	307	8	is	be	AUX
ap-7354	307	9	given	give	VERB
ap-7354	307	10	by	by	ADP
ap-7354	307	11	m	m	PROPN
ap-7354	307	12	=	=	ADJ
ap-7354	307	13	i	i	PRON
ap-7354	307	14	(	(	PUNCT
ap-7354	307	15	0	0	NUM
ap-7354	307	16	w12	w12	PROPN
ap-7354	307	17	w21	w21	PROPN
ap-7354	307	18	0	0	NUM
ap-7354	307	19	)	)	PUNCT
ap-7354	307	20	,	,	PUNCT
ap-7354	307	21	(	(	PUNCT
ap-7354	307	22	70	70	NUM
ap-7354	307	23	)	)	PUNCT
ap-7354	307	24	with	with	ADP
ap-7354	307	25	w12	w12	NOUN
ap-7354	307	26	=	=	PUNCT
ap-7354	307	27	−w21	−w21	PUNCT
ap-7354	307	28	=	=	X
ap-7354	307	29	<	<	X
ap-7354	307	30	nx	nx	X
ap-7354	307	31	,	,	PUNCT
ap-7354	307	32	ny	ny	PROPN
ap-7354	308	1	|	|	ADV
ap-7354	308	2	1	1	NUM
ap-7354	308	3	2{υv3	2{υv3	NUM
ap-7354	308	4	−	−	NOUN
ap-7354	308	5	(	(	PUNCT
ap-7354	308	6	v1	v1	NOUN
ap-7354	308	7	+	+	CCONJ
ap-7354	308	8	v2	v2	NOUN
ap-7354	308	9	)	)	PUNCT
ap-7354	308	10	}	}	PUNCT
ap-7354	309	1	|	|	ADV
ap-7354	309	2	n	n	DET
ap-7354	309	3	′	′	NUM
ap-7354	309	4	x	x	NOUN
ap-7354	309	5	,	,	PUNCT
ap-7354	309	6	n	n	PROPN
ap-7354	309	7	′	′	NOUN
ap-7354	309	8	y	y	INTJ
ap-7354	309	9	>	>	X
ap-7354	309	10	.	.	PUNCT
ap-7354	310	1	(	(	PUNCT
ap-7354	310	2	71	71	NUM
ap-7354	310	3	)	)	PUNCT
ap-7354	310	4	698	698	NUM
ap-7354	310	5	vol	vol	NOUN
ap-7354	310	6	.	.	PUNCT
ap-7354	311	1	61	61	NUM
ap-7354	311	2	no	no	NOUN
ap-7354	311	3	.	.	PUNCT
ap-7354	312	1	6/2021	6/2021	NUM
ap-7354	312	2	dirac	dirac	NOUN
ap-7354	312	3	oscillator	oscillator	NOUN
ap-7354	312	4	in	in	ADP
ap-7354	312	5	dynamical	dynamical	ADJ
ap-7354	312	6	noncommutative	noncommutative	ADJ
ap-7354	312	7	space	space	NOUN
ap-7354	312	8	the	the	DET
ap-7354	312	9	do	do	AUX
ap-7354	312	10	hamiltonian	hamiltonian	PROPN
ap-7354	312	11	hd	hd	PROPN
ap-7354	312	12	=	=	SYM
ap-7354	312	13	h0	h0	PROPN
ap-7354	312	14	+	+	NOUN
ap-7354	312	15	hθ	hθ	PROPN
ap-7354	312	16	+	+	NOUN
ap-7354	312	17	hτ	hτ	NOUN
ap-7354	312	18	may	may	AUX
ap-7354	312	19	be	be	AUX
ap-7354	312	20	represented	represent	VERB
ap-7354	312	21	by	by	ADP
ap-7354	312	22	a	a	DET
ap-7354	312	23	square	square	ADJ
ap-7354	312	24	matrix	matrix	NOUN
ap-7354	312	25	as	as	SCONJ
ap-7354	312	26	follows	follow	VERB
ap-7354	312	27	(	(	PUNCT
ap-7354	312	28	we	we	PRON
ap-7354	312	29	have	have	AUX
ap-7354	312	30	used	use	VERB
ap-7354	312	31	the	the	DET
ap-7354	312	32	basis	basis	NOUN
ap-7354	312	33	given	give	VERB
ap-7354	312	34	by	by	ADP
ap-7354	312	35	unperturbed	unperturbed	ADJ
ap-7354	312	36	energy	energy	NOUN
ap-7354	312	37	eigenkets	eigenket	NOUN
ap-7354	312	38	)	)	PUNCT
ap-7354	312	39	hd	hd	PROPN
ap-7354	312	40	≡	≡	PROPN
ap-7354	312	41	(	(	PUNCT
ap-7354	312	42	e	e	X
ap-7354	312	43	(	(	PUNCT
ap-7354	312	44	0	0	NUM
ap-7354	312	45	)	)	PUNCT
ap-7354	312	46	n,+	n,+	NUM
ap-7354	312	47	(	(	PUNCT
ap-7354	312	48	θ	θ	NOUN
ap-7354	312	49	)	)	PUNCT
ap-7354	312	50	iτw12	iτw12	NOUN
ap-7354	312	51	iτw21	iτw21	NOUN
ap-7354	312	52	e	e	NOUN
ap-7354	312	53	(	(	PUNCT
ap-7354	312	54	0	0	NUM
ap-7354	312	55	)	)	PUNCT
ap-7354	312	56	n,−	n,−	PROPN
ap-7354	312	57	(	(	PUNCT
ap-7354	312	58	θ	θ	NOUN
ap-7354	312	59	)	)	PUNCT
ap-7354	312	60	)	)	PUNCT
ap-7354	312	61	.	.	PUNCT
ap-7354	313	1	(	(	PUNCT
ap-7354	313	2	72	72	X
ap-7354	313	3	)	)	PUNCT
ap-7354	313	4	the	the	DET
ap-7354	313	5	eigenvalues	eigenvalue	NOUN
ap-7354	313	6	of	of	ADP
ap-7354	313	7	the	the	DET
ap-7354	313	8	problem	problem	NOUN
ap-7354	313	9	above	above	ADV
ap-7354	313	10	are	be	AUX
ap-7354	313	11	(	(	PUNCT
ap-7354	313	12	e1	e1	PROPN
ap-7354	313	13	e2	e2	PROPN
ap-7354	313	14	)	)	PUNCT
ap-7354	314	1	=	=	SYM
ap-7354	314	2	e	e	X
ap-7354	314	3	(	(	PUNCT
ap-7354	314	4	0	0	NUM
ap-7354	314	5	)	)	PUNCT
ap-7354	314	6	−	−	PROPN
ap-7354	315	1	+	+	CCONJ
ap-7354	315	2	e	e	X
ap-7354	315	3	(	(	PUNCT
ap-7354	315	4	0	0	NUM
ap-7354	315	5	)	)	PUNCT
ap-7354	315	6	+	+	CCONJ
ap-7354	315	7	2	2	NUM
ap-7354	315	8	±	±	NUM
ap-7354	315	9	√√√√(e(0	√√√√(e(0	PROPN
ap-7354	315	10	)	)	PUNCT
ap-7354	316	1	−	−	PROPN
ap-7354	317	1	−	−	PROPN
ap-7354	317	2	e	e	X
ap-7354	317	3	(	(	PUNCT
ap-7354	317	4	0	0	NUM
ap-7354	317	5	)	)	PUNCT
ap-7354	317	6	+	+	CCONJ
ap-7354	317	7	)	)	PUNCT
ap-7354	317	8	2	2	NUM
ap-7354	317	9	4	4	NUM
ap-7354	317	10	+	+	NUM
ap-7354	317	11	λ2	λ2	NOUN
ap-7354	317	12	|w12|2	|w12|2	NOUN
ap-7354	317	13	.	.	PUNCT
ap-7354	318	1	(	(	PUNCT
ap-7354	318	2	73	73	NUM
ap-7354	318	3	)	)	PUNCT
ap-7354	318	4	here	here	ADV
ap-7354	318	5	,	,	PUNCT
ap-7354	318	6	we	we	PRON
ap-7354	318	7	set	set	VERB
ap-7354	318	8	λ	λ	X
ap-7354	318	9	=	=	NOUN
ap-7354	318	10	iτ	iτ	NOUN
ap-7354	318	11	.	.	PUNCT
ap-7354	319	1	supposing	suppose	VERB
ap-7354	319	2	that	that	SCONJ
ap-7354	319	3	λ	λ	PROPN
ap-7354	319	4	|w12|	|w12|	PROPN
ap-7354	319	5	is	be	AUX
ap-7354	319	6	small	small	ADJ
ap-7354	319	7	as	as	SCONJ
ap-7354	319	8	compared	compare	VERB
ap-7354	319	9	to	to	ADP
ap-7354	319	10	relevant	relevant	ADJ
ap-7354	319	11	energy	energy	NOUN
ap-7354	319	12	scale	scale	NOUN
ap-7354	319	13	,	,	PUNCT
ap-7354	319	14	so	so	SCONJ
ap-7354	319	15	that	that	SCONJ
ap-7354	319	16	the	the	DET
ap-7354	319	17	difference	difference	NOUN
ap-7354	319	18	of	of	ADP
ap-7354	319	19	the	the	DET
ap-7354	319	20	energy	energy	NOUN
ap-7354	319	21	eigenvalues	eigenvalue	NOUN
ap-7354	319	22	of	of	ADP
ap-7354	319	23	the	the	DET
ap-7354	319	24	unperturbed	unperturbed	ADJ
ap-7354	319	25	system	system	NOUN
ap-7354	319	26	equals	equal	VERB
ap-7354	319	27	λ	λ	PROPN
ap-7354	319	28	|w12|	|w12|	PROPN
ap-7354	319	29	<	<	X
ap-7354	319	30	∣∣∣e(0	∣∣∣e(0	NOUN
ap-7354	319	31	)	)	PUNCT
ap-7354	320	1	−	−	NOUN
ap-7354	321	1	−	−	PROPN
ap-7354	321	2	e	e	X
ap-7354	321	3	(	(	PUNCT
ap-7354	321	4	0	0	NUM
ap-7354	321	5	)	)	PUNCT
ap-7354	321	6	+	+	CCONJ
ap-7354	321	7	∣∣∣	∣∣∣	ADJ
ap-7354	321	8	.	.	PUNCT
ap-7354	322	1	(	(	PUNCT
ap-7354	322	2	74	74	NUM
ap-7354	322	3	)	)	PUNCT
ap-7354	322	4	to	to	PART
ap-7354	322	5	obtain	obtain	VERB
ap-7354	322	6	the	the	DET
ap-7354	322	7	expansion	expansion	NOUN
ap-7354	322	8	of	of	ADP
ap-7354	322	9	the	the	DET
ap-7354	322	10	energy	energy	NOUN
ap-7354	322	11	eigenvalues	eigenvalue	VERB
ap-7354	322	12	in	in	ADP
ap-7354	322	13	the	the	DET
ap-7354	322	14	presence	presence	NOUN
ap-7354	322	15	of	of	ADP
ap-7354	322	16	a	a	DET
ap-7354	322	17	perturbation	perturbation	NOUN
ap-7354	322	18	,	,	PUNCT
ap-7354	322	19	namely	namely	ADV
ap-7354	322	20	(	(	PUNCT
ap-7354	322	21	a	a	DET
ap-7354	322	22	perturbation	perturbation	NOUN
ap-7354	322	23	expansion	expansion	NOUN
ap-7354	322	24	always	always	ADV
ap-7354	322	25	exists	exist	VERB
ap-7354	322	26	for	for	ADP
ap-7354	322	27	a	a	DET
ap-7354	322	28	sufficiently	sufficiently	ADV
ap-7354	322	29	weak	weak	ADJ
ap-7354	322	30	perturbation	perturbation	NOUN
ap-7354	322	31	)	)	PUNCT
ap-7354	322	32	e1	e1	NOUN
ap-7354	322	33	=	=	SYM
ap-7354	322	34	e	e	X
ap-7354	322	35	(	(	PUNCT
ap-7354	322	36	0	0	NUM
ap-7354	322	37	)	)	PUNCT
ap-7354	322	38	−	−	PROPN
ap-7354	323	1	+	+	CCONJ
ap-7354	323	2	λ2|w12|2	λ2|w12|2	NUM
ap-7354	323	3	e	e	X
ap-7354	323	4	(	(	PUNCT
ap-7354	323	5	0	0	NUM
ap-7354	323	6	)	)	PUNCT
ap-7354	323	7	−	−	NOUN
ap-7354	323	8	−e	−e	NOUN
ap-7354	323	9	(	(	PUNCT
ap-7354	323	10	0	0	NUM
ap-7354	323	11	)	)	PUNCT
ap-7354	324	1	+	+	PUNCT
ap-7354	324	2	+	+	CCONJ
ap-7354	324	3	.	.	PUNCT
ap-7354	324	4	.	.	PUNCT
ap-7354	324	5	.	.	PUNCT
ap-7354	325	1	e2	e2	PROPN
ap-7354	325	2	=	=	PUNCT
ap-7354	325	3	e	e	X
ap-7354	325	4	(	(	PUNCT
ap-7354	325	5	0	0	NUM
ap-7354	325	6	)	)	PUNCT
ap-7354	325	7	+	+	CCONJ
ap-7354	326	1	+	+	CCONJ
ap-7354	326	2	λ2|w12|2	λ2|w12|2	NUM
ap-7354	326	3	e	e	X
ap-7354	326	4	(	(	PUNCT
ap-7354	326	5	0	0	NUM
ap-7354	326	6	)	)	PUNCT
ap-7354	326	7	+	+	CCONJ
ap-7354	326	8	−e	−e	NOUN
ap-7354	326	9	(	(	PUNCT
ap-7354	326	10	0	0	NUM
ap-7354	326	11	)	)	PUNCT
ap-7354	326	12	−	−	PROPN
ap-7354	327	1	+	+	CCONJ
ap-7354	327	2	.	.	PUNCT
ap-7354	327	3	.	.	PUNCT
ap-7354	327	4	.	.	PUNCT
ap-7354	328	1	(	(	PUNCT
ap-7354	328	2	75	75	NUM
ap-7354	328	3	)	)	PUNCT
ap-7354	328	4	we	we	PRON
ap-7354	328	5	terminate	terminate	VERB
ap-7354	328	6	the	the	DET
ap-7354	328	7	calculation	calculation	NOUN
ap-7354	328	8	by	by	ADP
ap-7354	328	9	the	the	DET
ap-7354	328	10	radius	radius	NOUN
ap-7354	328	11	of	of	ADP
ap-7354	328	12	convergence	convergence	NOUN
ap-7354	328	13	of	of	ADP
ap-7354	328	14	series	series	NOUN
ap-7354	328	15	expansion	expansion	NOUN
ap-7354	328	16	(	(	PUNCT
ap-7354	328	17	75	75	NUM
ap-7354	328	18	)	)	PUNCT
ap-7354	328	19	,	,	PUNCT
ap-7354	328	20	so	so	CCONJ
ap-7354	328	21	while	while	SCONJ
ap-7354	328	22	λ	λ	NOUN
ap-7354	328	23	is	be	AUX
ap-7354	328	24	a	a	DET
ap-7354	328	25	complex	complex	ADJ
ap-7354	328	26	variable	variable	NOUN
ap-7354	328	27	,	,	PUNCT
ap-7354	328	28	λ	λ	PROPN
ap-7354	328	29	is	be	AUX
ap-7354	328	30	increased	increase	VERB
ap-7354	328	31	from	from	ADP
ap-7354	328	32	zero	zero	NUM
ap-7354	328	33	,	,	PUNCT
ap-7354	328	34	branch	branch	NOUN
ap-7354	328	35	points	point	NOUN
ap-7354	328	36	are	be	AUX
ap-7354	328	37	encoutered	encoutere	VERB
ap-7354	328	38	at	at	ADP
ap-7354	328	39	[	[	X
ap-7354	328	40	34	34	NUM
ap-7354	328	41	]	]	X
ap-7354	328	42	λ	λ	X
ap-7354	328	43	|w12|	|w12|	PROPN
ap-7354	329	1	=	=	PUNCT
ap-7354	329	2	±i	±i	PROPN
ap-7354	329	3	(	(	PUNCT
ap-7354	329	4	e	e	X
ap-7354	329	5	(	(	PUNCT
ap-7354	329	6	0	0	NUM
ap-7354	329	7	)	)	PUNCT
ap-7354	329	8	−	−	NOUN
ap-7354	329	9	−	−	PROPN
ap-7354	329	10	e	e	X
ap-7354	329	11	(	(	PUNCT
ap-7354	329	12	0	0	NUM
ap-7354	329	13	)	)	PUNCT
ap-7354	329	14	+	+	CCONJ
ap-7354	329	15	)	)	PUNCT
ap-7354	329	16	2	2	NUM
ap-7354	329	17	,	,	PUNCT
ap-7354	329	18	(	(	PUNCT
ap-7354	329	19	76	76	NUM
ap-7354	329	20	)	)	PUNCT
ap-7354	329	21	the	the	DET
ap-7354	329	22	condition	condition	NOUN
ap-7354	329	23	for	for	ADP
ap-7354	329	24	the	the	DET
ap-7354	329	25	convergence	convergence	NOUN
ap-7354	329	26	of	of	ADP
ap-7354	329	27	(	(	PUNCT
ap-7354	329	28	75	75	NUM
ap-7354	329	29	)	)	PUNCT
ap-7354	329	30	for	for	ADP
ap-7354	329	31	the	the	DET
ap-7354	329	32	λ	λ	PROPN
ap-7354	329	33	=	=	SYM
ap-7354	329	34	1	1	NUM
ap-7354	329	35	full	full	ADJ
ap-7354	329	36	strength	strength	NOUN
ap-7354	329	37	case	case	NOUN
ap-7354	329	38	is	be	AUX
ap-7354	329	39	|w12|	|w12|	PROPN
ap-7354	329	40	=	=	SYM
ap-7354	329	41	∣∣∣e(0	∣∣∣e(0	NOUN
ap-7354	329	42	)	)	PUNCT
ap-7354	329	43	−	−	NOUN
ap-7354	330	1	−	−	PROPN
ap-7354	330	2	e	e	X
ap-7354	330	3	(	(	PUNCT
ap-7354	330	4	0	0	NUM
ap-7354	330	5	)	)	PUNCT
ap-7354	330	6	+	+	CCONJ
ap-7354	330	7	∣∣∣	∣∣∣	ADJ
ap-7354	330	8	2	2	NUM
ap-7354	330	9	.	.	PUNCT
ap-7354	331	1	(	(	PUNCT
ap-7354	331	2	77	77	NUM
ap-7354	331	3	)	)	PUNCT
ap-7354	331	4	if	if	SCONJ
ap-7354	331	5	this	this	DET
ap-7354	331	6	condition	condition	NOUN
ap-7354	331	7	is	be	AUX
ap-7354	331	8	not	not	PART
ap-7354	331	9	met	meet	VERB
ap-7354	331	10	,	,	PUNCT
ap-7354	331	11	the	the	DET
ap-7354	331	12	expansion	expansion	NOUN
ap-7354	331	13	(	(	PUNCT
ap-7354	331	14	75	75	NUM
ap-7354	331	15	)	)	PUNCT
ap-7354	331	16	is	be	AUX
ap-7354	331	17	meaningless	meaningless	ADJ
ap-7354	331	18	.	.	PUNCT
ap-7354	332	1	it	it	PRON
ap-7354	332	2	can	can	AUX
ap-7354	332	3	be	be	AUX
ap-7354	332	4	checked	check	VERB
ap-7354	332	5	that	that	SCONJ
ap-7354	332	6	all	all	DET
ap-7354	332	7	the	the	DET
ap-7354	332	8	results	result	NOUN
ap-7354	332	9	of	of	ADP
ap-7354	332	10	the	the	DET
ap-7354	332	11	nc	nc	PROPN
ap-7354	332	12	case	case	NOUN
ap-7354	332	13	can	can	AUX
ap-7354	332	14	be	be	AUX
ap-7354	332	15	obtained	obtain	VERB
ap-7354	332	16	from	from	ADP
ap-7354	332	17	the	the	DET
ap-7354	332	18	dnc	dnc	PROPN
ap-7354	332	19	case	case	NOUN
ap-7354	332	20	directly	directly	ADV
ap-7354	332	21	by	by	ADP
ap-7354	332	22	taking	take	VERB
ap-7354	332	23	the	the	DET
ap-7354	332	24	limit	limit	NOUN
ap-7354	332	25	of	of	ADP
ap-7354	332	26	τ	τ	PROPN
ap-7354	332	27	→	→	SYM
ap-7354	332	28	0	0	NUM
ap-7354	332	29	,	,	PUNCT
ap-7354	332	30	for	for	ADP
ap-7354	332	31	instance	instance	NOUN
ap-7354	332	32	,	,	PUNCT
ap-7354	332	33	equations	equation	NOUN
ap-7354	332	34	(	(	PUNCT
ap-7354	332	35	51	51	NUM
ap-7354	332	36	)	)	PUNCT
ap-7354	332	37	and	and	CCONJ
ap-7354	332	38	(	(	PUNCT
ap-7354	332	39	52	52	NUM
ap-7354	332	40	)	)	PUNCT
ap-7354	332	41	give	give	VERB
ap-7354	332	42	the	the	DET
ap-7354	332	43	same	same	ADJ
ap-7354	332	44	values	value	NOUN
ap-7354	332	45	as	as	ADP
ap-7354	332	46	the	the	DET
ap-7354	332	47	eigenvalues	eigenvalue	NOUN
ap-7354	332	48	and	and	CCONJ
ap-7354	332	49	eigenvectors	eigenvector	NOUN
ap-7354	332	50	in	in	ADP
ap-7354	332	51	the	the	DET
ap-7354	332	52	nc	nc	PROPN
ap-7354	332	53	space	space	NOUN
ap-7354	332	54	,	,	PUNCT
ap-7354	332	55	i.e.	i.e.	X
ap-7354	332	56	,	,	PUNCT
ap-7354	332	57	equations	equation	NOUN
ap-7354	332	58	(	(	PUNCT
ap-7354	332	59	47	47	NUM
ap-7354	332	60	)	)	PUNCT
ap-7354	332	61	and	and	CCONJ
ap-7354	332	62	(	(	PUNCT
ap-7354	332	63	49	49	NUM
ap-7354	332	64	)	)	PUNCT
ap-7354	332	65	,	,	PUNCT
ap-7354	332	66	respectively	respectively	ADV
ap-7354	332	67	.	.	PUNCT
ap-7354	333	1	it	it	PRON
ap-7354	333	2	may	may	AUX
ap-7354	333	3	be	be	AUX
ap-7354	333	4	also	also	ADV
ap-7354	333	5	useful	useful	ADJ
ap-7354	333	6	to	to	PART
ap-7354	333	7	mention	mention	VERB
ap-7354	333	8	that	that	SCONJ
ap-7354	333	9	the	the	DET
ap-7354	333	10	do	do	NOUN
ap-7354	333	11	in	in	ADP
ap-7354	333	12	deformed	deform	VERB
ap-7354	333	13	spaces	space	NOUN
ap-7354	333	14	(	(	PUNCT
ap-7354	333	15	including	include	VERB
ap-7354	333	16	nc	nc	PROPN
ap-7354	333	17	spaces	space	NOUN
ap-7354	333	18	)	)	PUNCT
ap-7354	333	19	has	have	AUX
ap-7354	333	20	been	be	AUX
ap-7354	333	21	investigated	investigate	VERB
ap-7354	333	22	in	in	ADP
ap-7354	333	23	[	[	NOUN
ap-7354	333	24	36–43	36–43	NUM
ap-7354	333	25	]	]	PUNCT
ap-7354	333	26	.	.	PUNCT
ap-7354	334	1	we	we	PRON
ap-7354	334	2	can	can	AUX
ap-7354	334	3	regard	regard	VERB
ap-7354	334	4	equation	equation	NOUN
ap-7354	334	5	(	(	PUNCT
ap-7354	334	6	75	75	NUM
ap-7354	334	7	)	)	PUNCT
ap-7354	334	8	as	as	ADP
ap-7354	334	9	the	the	DET
ap-7354	334	10	eigenvalues	eigenvalue	NOUN
ap-7354	334	11	of	of	ADP
ap-7354	334	12	our	our	PRON
ap-7354	334	13	system	system	NOUN
ap-7354	334	14	,	,	PUNCT
ap-7354	334	15	where	where	SCONJ
ap-7354	334	16	we	we	PRON
ap-7354	334	17	restrict	restrict	VERB
ap-7354	334	18	ourselves	ourselves	PRON
ap-7354	334	19	to	to	ADP
ap-7354	334	20	the	the	DET
ap-7354	334	21	first	first	ADJ
ap-7354	334	22	-	-	PUNCT
ap-7354	334	23	order	order	NOUN
ap-7354	334	24	correction	correction	NOUN
ap-7354	334	25	to	to	ADP
ap-7354	334	26	the	the	DET
ap-7354	334	27	eigenvalues	eigenvalue	NOUN
ap-7354	334	28	and	and	CCONJ
ap-7354	334	29	eigenvectors	eigenvector	NOUN
ap-7354	334	30	,	,	PUNCT
ap-7354	334	31	which	which	PRON
ap-7354	334	32	leads	lead	VERB
ap-7354	334	33	the	the	DET
ap-7354	334	34	energy	energy	NOUN
ap-7354	334	35	shift	shift	NOUN
ap-7354	334	36	for	for	ADP
ap-7354	334	37	the	the	DET
ap-7354	334	38	ground	ground	NOUN
ap-7354	334	39	state	state	NOUN
ap-7354	334	40	.	.	PUNCT
ap-7354	335	1	besides	besides	ADV
ap-7354	335	2	,	,	PUNCT
ap-7354	335	3	it	it	PRON
ap-7354	335	4	is	be	AUX
ap-7354	335	5	easy	easy	ADJ
ap-7354	335	6	to	to	PART
ap-7354	335	7	obtain	obtain	VERB
ap-7354	335	8	the	the	DET
ap-7354	335	9	eigensolutions	eigensolution	NOUN
ap-7354	335	10	for	for	ADP
ap-7354	335	11	excited	excited	ADJ
ap-7354	335	12	states	state	NOUN
ap-7354	335	13	.	.	PUNCT
ap-7354	336	1	it	it	PRON
ap-7354	336	2	is	be	AUX
ap-7354	336	3	interesting	interesting	ADJ
ap-7354	336	4	to	to	PART
ap-7354	336	5	illustrate	illustrate	VERB
ap-7354	336	6	the	the	DET
ap-7354	336	7	dnc	dnc	PROPN
ap-7354	336	8	effect	effect	NOUN
ap-7354	336	9	on	on	ADP
ap-7354	336	10	do	do	AUX
ap-7354	336	11	energy	energy	NOUN
ap-7354	336	12	levels	level	NOUN
ap-7354	336	13	.	.	PUNCT
ap-7354	337	1	this	this	DET
ap-7354	337	2	effect	effect	NOUN
ap-7354	337	3	is	be	AUX
ap-7354	337	4	reduced	reduce	VERB
ap-7354	337	5	in	in	ADP
ap-7354	337	6	the	the	DET
ap-7354	337	7	energy	energy	NOUN
ap-7354	337	8	shifts	shift	NOUN
ap-7354	337	9	obtained	obtain	VERB
ap-7354	337	10	,	,	PUNCT
ap-7354	337	11	hence	hence	ADV
ap-7354	337	12	we	we	PRON
ap-7354	337	13	do	do	VERB
ap-7354	337	14	the	the	DET
ap-7354	337	15	following	follow	VERB
ap-7354	337	16	sample	sample	NOUN
ap-7354	337	17	,	,	PUNCT
ap-7354	337	18	with	with	ADP
ap-7354	337	19	a1	a1	NOUN
ap-7354	337	20	=	=	NOUN
ap-7354	337	21	υ	υ	NOUN
ap-7354	337	22	2	2	NUM
ap-7354	337	23	(	(	PUNCT
ap-7354	338	1	ℏ	ℏ	PROPN
ap-7354	338	2	2mω	2mω	NOUN
ap-7354	338	3	)	)	PUNCT
ap-7354	338	4	3	3	NUM
ap-7354	338	5	2	2	NUM
ap-7354	338	6	,	,	PUNCT
ap-7354	338	7	a2	a2	PROPN
ap-7354	338	8	=	=	PROPN
ap-7354	338	9	iℏ	iℏ	ADP
ap-7354	338	10	2ω	2ω	NUM
ap-7354	338	11	(	(	PUNCT
ap-7354	338	12	ℏ	ℏ	NOUN
ap-7354	338	13	2mω	2mω	ADJ
ap-7354	338	14	)	)	PUNCT
ap-7354	338	15	1	1	NUM
ap-7354	338	16	2	2	NUM
ap-7354	338	17	,	,	PUNCT
ap-7354	338	18	a3	a3	NOUN
ap-7354	338	19	=	=	SYM
ap-7354	338	20	iℏ	iℏ	NOUN
ap-7354	338	21	(	(	PUNCT
ap-7354	338	22	ℏ	ℏ	NOUN
ap-7354	338	23	mω	mω	NOUN
ap-7354	338	24	)	)	PUNCT
ap-7354	338	25	1	1	NUM
ap-7354	338	26	2	2	NUM
ap-7354	338	27	,	,	PUNCT
ap-7354	338	28	a4	a4	NOUN
ap-7354	338	29	=	=	PUNCT
ap-7354	338	30	iℏ	iℏ	ADP
ap-7354	338	31	2	2	NUM
ap-7354	338	32	(	(	PUNCT
ap-7354	338	33	ℏ	ℏ	NOUN
ap-7354	338	34	mω	mω	NOUN
ap-7354	338	35	)	)	PUNCT
ap-7354	338	36	1	1	NUM
ap-7354	338	37	2	2	NUM
ap-7354	338	38	.	.	PUNCT
ap-7354	339	1	(	(	PUNCT
ap-7354	339	2	78	78	NUM
ap-7354	339	3	)	)	PUNCT
ap-7354	339	4	in	in	ADP
ap-7354	339	5	table	table	NOUN
ap-7354	339	6	1	1	NUM
ap-7354	339	7	,	,	PUNCT
ap-7354	339	8	all	all	DET
ap-7354	339	9	numerical	numerical	ADJ
ap-7354	339	10	values	value	NOUN
ap-7354	339	11	of	of	ADP
ap-7354	339	12	the	the	DET
ap-7354	339	13	energy	energy	NOUN
ap-7354	339	14	are	be	AUX
ap-7354	339	15	in	in	ADP
ap-7354	339	16	units	unit	NOUN
ap-7354	339	17	of	of	ADP
ap-7354	339	18	ev	ev	PROPN
ap-7354	339	19	.	.	PUNCT
ap-7354	340	1	it	it	PRON
ap-7354	340	2	may	may	AUX
ap-7354	340	3	be	be	AUX
ap-7354	340	4	worth	worth	ADJ
ap-7354	340	5	to	to	PART
ap-7354	340	6	underline	underline	VERB
ap-7354	340	7	that	that	DET
ap-7354	340	8	thanks	thank	NOUN
ap-7354	340	9	to	to	ADP
ap-7354	340	10	the	the	DET
ap-7354	340	11	kronecker	kronecker	NOUN
ap-7354	340	12	’s	’s	PART
ap-7354	340	13	delta	delta	NOUN
ap-7354	340	14	,	,	PUNCT
ap-7354	340	15	the	the	DET
ap-7354	340	16	elements	element	NOUN
ap-7354	340	17	of	of	ADP
ap-7354	340	18	the	the	DET
ap-7354	340	19	perturbed	perturb	VERB
ap-7354	340	20	hamiltonian	hamiltonian	NOUN
ap-7354	340	21	will	will	AUX
ap-7354	340	22	seldom	seldom	ADV
ap-7354	340	23	take	take	VERB
ap-7354	340	24	many	many	ADJ
ap-7354	340	25	values	value	NOUN
ap-7354	340	26	.	.	PUNCT
ap-7354	341	1	now	now	ADV
ap-7354	341	2	,	,	PUNCT
ap-7354	341	3	the	the	DET
ap-7354	341	4	dnc	dnc	PROPN
ap-7354	341	5	and	and	CCONJ
ap-7354	341	6	non	non	ADJ
ap-7354	341	7	-	-	ADJ
ap-7354	341	8	dnc	dnc	ADJ
ap-7354	341	9	effects	effect	NOUN
ap-7354	341	10	on	on	ADP
ap-7354	341	11	the	the	DET
ap-7354	341	12	energy	energy	NOUN
ap-7354	341	13	levels	level	NOUN
ap-7354	341	14	of	of	ADP
ap-7354	341	15	the	the	DET
ap-7354	341	16	do	do	NOUN
ap-7354	341	17	are	be	AUX
ap-7354	341	18	illustrated	illustrate	VERB
ap-7354	341	19	in	in	ADP
ap-7354	341	20	fig	fig	NOUN
ap-7354	341	21	.	.	PUNCT
ap-7354	342	1	3	3	X
ap-7354	342	2	.	.	X
ap-7354	342	3	the	the	DET
ap-7354	342	4	upper	upper	ADJ
ap-7354	342	5	bound	bind	VERB
ap-7354	342	6	on	on	ADP
ap-7354	342	7	the	the	DET
ap-7354	342	8	value	value	NOUN
ap-7354	342	9	of	of	ADP
ap-7354	342	10	the	the	DET
ap-7354	342	11	nc	nc	PROPN
ap-7354	342	12	parameter	parameter	PROPN
ap-7354	342	13	θ	θ	PROPN
ap-7354	342	14	is	be	AUX
ap-7354	342	15	√	√	NUM
ap-7354	342	16	θ	θ	NOUN
ap-7354	342	17	≤	≤	NUM
ap-7354	342	18	2	2	NUM
ap-7354	342	19	×	×	NOUN
ap-7354	342	20	10−20	10−20	NUM
ap-7354	342	21	m	m	NOUN
ap-7354	343	1	[	[	X
ap-7354	343	2	44	44	NUM
ap-7354	343	3	]	]	PUNCT
ap-7354	343	4	,	,	PUNCT
ap-7354	343	5	as	as	ADV
ap-7354	343	6	well	well	ADV
ap-7354	343	7	for	for	ADP
ap-7354	343	8	τ	τ	PROPN
ap-7354	343	9	is	be	AUX
ap-7354	343	10	√	√	ADV
ap-7354	343	11	τ	τ	PROPN
ap-7354	343	12	≤	≤	NUM
ap-7354	343	13	10−17	10−17	NUM
ap-7354	343	14	ev	ev	X
ap-7354	344	1	[	[	X
ap-7354	344	2	45	45	NUM
ap-7354	344	3	]	]	PUNCT
ap-7354	344	4	.	.	PUNCT
ap-7354	345	1	the	the	DET
ap-7354	345	2	bound	bind	VERB
ap-7354	345	3	on	on	ADP
ap-7354	345	4	√	√	PROPN
ap-7354	345	5	τ	τ	PROPN
ap-7354	345	6	is	be	AUX
ap-7354	345	7	consistent	consistent	ADJ
ap-7354	345	8	with	with	ADP
ap-7354	345	9	the	the	DET
ap-7354	345	10	accuracy	accuracy	NOUN
ap-7354	345	11	in	in	ADP
ap-7354	345	12	the	the	DET
ap-7354	345	13	energy	energy	NOUN
ap-7354	345	14	measurement	measurement	NOUN
ap-7354	345	15	10−12	10−12	PROPN
ap-7354	345	16	ev	ev	PROPN
ap-7354	345	17	.	.	PROPN
ap-7354	345	18	699	699	NUM
ap-7354	345	19	ilyas	ilyas	PROPN
ap-7354	345	20	haouam	haouam	PROPN
ap-7354	345	21	acta	acta	PROPN
ap-7354	345	22	polytechnica	polytechnica	PROPN
ap-7354	345	23	(	(	PUNCT
ap-7354	345	24	nx	nx	PROPN
ap-7354	345	25	,	,	PUNCT
ap-7354	345	26	ny	ny	PROPN
ap-7354	345	27	,	,	PUNCT
ap-7354	345	28	n	n	NOUN
ap-7354	345	29	′	′	NUM
ap-7354	345	30	x	x	NOUN
ap-7354	345	31	,	,	PUNCT
ap-7354	345	32	n	n	PROPN
ap-7354	345	33	′	′	NUM
ap-7354	345	34	y	y	PROPN
ap-7354	345	35	)	)	PUNCT
ap-7354	345	36	w12	w12	PROPN
ap-7354	345	37	e1	e1	PROPN
ap-7354	345	38	e2	e2	PROPN
ap-7354	345	39	△	△	PROPN
ap-7354	345	40	e	e	X
ap-7354	345	41	(	(	PUNCT
ap-7354	345	42	1	1	NUM
ap-7354	345	43	,	,	PUNCT
ap-7354	345	44	1	1	NUM
ap-7354	345	45	,	,	PUNCT
ap-7354	345	46	1	1	NUM
ap-7354	345	47	,	,	PUNCT
ap-7354	345	48	1	1	NUM
ap-7354	345	49	)	)	PUNCT
ap-7354	345	50	0	0	PUNCT
ap-7354	346	1	−5	−5	NOUN
ap-7354	346	2	,	,	PUNCT
ap-7354	346	3	11.105	11.105	NUM
ap-7354	346	4	5	5	NUM
ap-7354	346	5	,	,	PUNCT
ap-7354	346	6	11.105	11.105	NUM
ap-7354	346	7	0	0	NUM
ap-7354	347	1	(	(	PUNCT
ap-7354	347	2	1	1	NUM
ap-7354	347	3	,	,	PUNCT
ap-7354	347	4	0	0	NUM
ap-7354	347	5	,	,	PUNCT
ap-7354	347	6	0	0	NUM
ap-7354	347	7	,	,	PUNCT
ap-7354	347	8	0	0	NUM
ap-7354	347	9	)	)	PUNCT
ap-7354	347	10	a1	a1	NOUN
ap-7354	347	11	−5	−5	NOUN
ap-7354	347	12	,	,	PUNCT
ap-7354	347	13	11.105	11.105	NUM
ap-7354	347	14	+	+	NUM
ap-7354	347	15	a2	a2	PROPN
ap-7354	347	16	1τ2	1τ2	NUM
ap-7354	347	17	10,22.105	10,22.105	NUM
ap-7354	347	18	5	5	NUM
ap-7354	347	19	,	,	PUNCT
ap-7354	347	20	11.105	11.105	NUM
ap-7354	347	21	−	−	PROPN
ap-7354	347	22	a2	a2	PROPN
ap-7354	347	23	1τ2	1τ2	NUM
ap-7354	347	24	10,22.105	10,22.105	PROPN
ap-7354	347	25	a2	a2	PROPN
ap-7354	347	26	1τ2	1τ2	NUM
ap-7354	347	27	10,22.105	10,22.105	NUM
ap-7354	347	28	(	(	PUNCT
ap-7354	347	29	0	0	NUM
ap-7354	347	30	,	,	PUNCT
ap-7354	347	31	0	0	NUM
ap-7354	347	32	,	,	PUNCT
ap-7354	347	33	0	0	NUM
ap-7354	347	34	,	,	PUNCT
ap-7354	347	35	1	1	X
ap-7354	347	36	)	)	PUNCT
ap-7354	347	37	a2	a2	NOUN
ap-7354	347	38	−5	−5	ADP
ap-7354	347	39	,	,	PUNCT
ap-7354	347	40	11.105	11.105	NUM
ap-7354	347	41	+	+	NUM
ap-7354	347	42	a2	a2	PROPN
ap-7354	347	43	2τ2	2τ2	NUM
ap-7354	347	44	10,22.105	10,22.105	NUM
ap-7354	347	45	5	5	NUM
ap-7354	347	46	,	,	PUNCT
ap-7354	347	47	11.105	11.105	NUM
ap-7354	347	48	−	−	PROPN
ap-7354	347	49	a2	a2	PROPN
ap-7354	347	50	2τ2	2τ2	NUM
ap-7354	348	1	10,22.105	10,22.105	NUM
ap-7354	348	2	a2	a2	PROPN
ap-7354	348	3	2τ2	2τ2	NUM
ap-7354	348	4	10,22.105	10,22.105	NUM
ap-7354	348	5	(	(	PUNCT
ap-7354	348	6	0	0	NUM
ap-7354	348	7	,	,	PUNCT
ap-7354	348	8	1	1	NUM
ap-7354	348	9	,	,	PUNCT
ap-7354	348	10	0	0	NUM
ap-7354	348	11	,	,	PUNCT
ap-7354	348	12	2	2	NUM
ap-7354	348	13	)	)	PUNCT
ap-7354	348	14	a3	a3	NOUN
ap-7354	348	15	−5	−5	ADP
ap-7354	348	16	,	,	PUNCT
ap-7354	348	17	11.105	11.105	NUM
ap-7354	348	18	+	+	NUM
ap-7354	348	19	a2	a2	PROPN
ap-7354	348	20	3τ2	3τ2	PROPN
ap-7354	348	21	10,22.105	10,22.105	NUM
ap-7354	348	22	5	5	NUM
ap-7354	348	23	,	,	PUNCT
ap-7354	348	24	11.105	11.105	NUM
ap-7354	348	25	−	−	PROPN
ap-7354	348	26	a2	a2	PROPN
ap-7354	348	27	3τ2	3τ2	PROPN
ap-7354	348	28	10,22.105	10,22.105	PROPN
ap-7354	348	29	a2	a2	PROPN
ap-7354	348	30	3τ2	3τ2	PROPN
ap-7354	348	31	10,22.105	10,22.105	PROPN
ap-7354	348	32	(	(	PUNCT
ap-7354	348	33	0	0	NUM
ap-7354	348	34	,	,	PUNCT
ap-7354	348	35	2	2	NUM
ap-7354	348	36	,	,	PUNCT
ap-7354	348	37	0	0	NUM
ap-7354	348	38	,	,	PUNCT
ap-7354	348	39	1	1	NUM
ap-7354	348	40	)	)	PUNCT
ap-7354	348	41	-a4	-a4	VERB
ap-7354	348	42	−5	−5	ADV
ap-7354	348	43	,	,	PUNCT
ap-7354	348	44	11.105	11.105	NUM
ap-7354	348	45	+	+	NUM
ap-7354	348	46	a2	a2	PROPN
ap-7354	348	47	4τ2	4τ2	NOUN
ap-7354	348	48	10,22.105	10,22.105	NUM
ap-7354	348	49	5	5	NUM
ap-7354	348	50	,	,	PUNCT
ap-7354	348	51	11.105	11.105	NUM
ap-7354	348	52	−	−	PROPN
ap-7354	348	53	a2	a2	PROPN
ap-7354	348	54	4τ2	4τ2	NUM
ap-7354	348	55	10,22.105	10,22.105	PROPN
ap-7354	348	56	a2	a2	PROPN
ap-7354	348	57	4τ2	4τ2	NOUN
ap-7354	349	1	10,22.105	10,22.105	NUM
ap-7354	349	2	table	table	NOUN
ap-7354	349	3	1	1	NUM
ap-7354	349	4	.	.	PUNCT
ap-7354	349	5	energy	energy	NOUN
ap-7354	349	6	levels	level	NOUN
ap-7354	349	7	due	due	ADP
ap-7354	349	8	to	to	ADP
ap-7354	349	9	dnc	dnc	PROPN
ap-7354	349	10	space	space	NOUN
ap-7354	349	11	,	,	PUNCT
ap-7354	349	12	where	where	SCONJ
ap-7354	349	13	we	we	PRON
ap-7354	349	14	suffice	suffice	VERB
ap-7354	349	15	with	with	ADP
ap-7354	349	16	eigenvalues	eigenvalue	VERB
ap-7354	349	17	corrections	correction	NOUN
ap-7354	349	18	to	to	ADP
ap-7354	349	19	the	the	DET
ap-7354	349	20	ground	ground	NOUN
ap-7354	349	21	state	state	NOUN
ap-7354	349	22	,	,	PUNCT
ap-7354	349	23	i.e.	i.e.	X
ap-7354	349	24	e1,2	e1,2	ADJ
ap-7354	349	25	=	=	SYM
ap-7354	349	26	±mc2	±mc2	NOUN
ap-7354	349	27	.	.	PUNCT
ap-7354	350	1	figure	figure	NOUN
ap-7354	350	2	3	3	NUM
ap-7354	350	3	.	.	X
ap-7354	350	4	diagram	diagram	NOUN
ap-7354	350	5	of	of	ADP
ap-7354	350	6	splittings	splitting	NOUN
ap-7354	350	7	for	for	ADP
ap-7354	350	8	energy	energy	NOUN
ap-7354	350	9	levels	level	NOUN
ap-7354	350	10	due	due	ADP
ap-7354	350	11	to	to	ADP
ap-7354	350	12	dnc	dnc	PROPN
ap-7354	350	13	and	and	CCONJ
ap-7354	350	14	non	non	ADJ
ap-7354	350	15	-	-	ADJ
ap-7354	350	16	dnc	dnc	ADJ
ap-7354	350	17	spaces	space	NOUN
ap-7354	350	18	.	.	PUNCT
ap-7354	351	1	it	it	PRON
ap-7354	351	2	is	be	AUX
ap-7354	351	3	important	important	ADJ
ap-7354	351	4	to	to	PART
ap-7354	351	5	clarify	clarify	VERB
ap-7354	351	6	that	that	SCONJ
ap-7354	351	7	the	the	DET
ap-7354	351	8	presence	presence	NOUN
ap-7354	351	9	of	of	ADP
ap-7354	351	10	τ2	τ2	NOUN
ap-7354	351	11	in	in	ADP
ap-7354	351	12	the	the	DET
ap-7354	351	13	eigenvalues	eigenvalue	NOUN
ap-7354	351	14	is	be	AUX
ap-7354	351	15	not	not	PART
ap-7354	351	16	due	due	ADJ
ap-7354	351	17	to	to	ADP
ap-7354	351	18	the	the	DET
ap-7354	351	19	action	action	NOUN
ap-7354	351	20	of	of	ADP
ap-7354	351	21	the	the	DET
ap-7354	351	22	second	second	ADJ
ap-7354	351	23	-	-	PUNCT
ap-7354	351	24	order	order	NOUN
ap-7354	351	25	correction	correction	NOUN
ap-7354	351	26	,	,	PUNCT
ap-7354	351	27	but	but	CCONJ
ap-7354	351	28	rather	rather	ADV
ap-7354	351	29	due	due	ADP
ap-7354	351	30	to	to	ADP
ap-7354	351	31	the	the	DET
ap-7354	351	32	dirac	dirac	NOUN
ap-7354	351	33	matrices	matrix	NOUN
ap-7354	351	34	in	in	ADP
ap-7354	351	35	the	the	DET
ap-7354	351	36	perturbed	perturb	VERB
ap-7354	351	37	hamiltonian	hamiltonian	ADJ
ap-7354	351	38	term	term	NOUN
ap-7354	351	39	.	.	PUNCT
ap-7354	352	1	in	in	ADP
ap-7354	352	2	fig	fig	NOUN
ap-7354	352	3	.	.	PUNCT
ap-7354	353	1	3	3	NUM
ap-7354	353	2	,	,	PUNCT
ap-7354	353	3	we	we	PRON
ap-7354	353	4	see	see	VERB
ap-7354	353	5	the	the	DET
ap-7354	353	6	energy	energy	NOUN
ap-7354	353	7	levels	level	NOUN
ap-7354	353	8	are	be	AUX
ap-7354	353	9	splitting	split	VERB
ap-7354	353	10	as	as	SCONJ
ap-7354	353	11	the	the	DET
ap-7354	353	12	θ	θ	PROPN
ap-7354	353	13	and	and	CCONJ
ap-7354	353	14	τ	τ	PROPN
ap-7354	353	15	parameters	parameter	NOUN
ap-7354	353	16	turn	turn	VERB
ap-7354	353	17	on	on	ADP
ap-7354	353	18	.	.	PUNCT
ap-7354	354	1	values	value	NOUN
ap-7354	354	2	of	of	ADP
ap-7354	354	3	the	the	DET
ap-7354	354	4	eigenvalues	eigenvalue	NOUN
ap-7354	354	5	e1	e1	PROPN
ap-7354	354	6	and	and	CCONJ
ap-7354	354	7	e2	e2	PROPN
ap-7354	354	8	are	be	AUX
ap-7354	354	9	shown	show	VERB
ap-7354	354	10	in	in	ADP
ap-7354	354	11	table	table	NOUN
ap-7354	354	12	1	1	NUM
ap-7354	354	13	.	.	PUNCT
ap-7354	355	1	first	first	ADV
ap-7354	355	2	,	,	PUNCT
ap-7354	355	3	in	in	ADP
ap-7354	355	4	fig	fig	NOUN
ap-7354	355	5	.	.	PUNCT
ap-7354	356	1	3	3	NUM
ap-7354	356	2	,	,	PUNCT
ap-7354	356	3	we	we	PRON
ap-7354	356	4	show	show	VERB
ap-7354	356	5	the	the	DET
ap-7354	356	6	effect	effect	NOUN
ap-7354	356	7	of	of	ADP
ap-7354	356	8	the	the	DET
ap-7354	356	9	nc	nc	PROPN
ap-7354	356	10	space	space	NOUN
ap-7354	356	11	when	when	SCONJ
ap-7354	356	12	the	the	DET
ap-7354	356	13	perturbation	perturbation	NOUN
ap-7354	356	14	parameter	parameter	NOUN
ap-7354	356	15	is	be	AUX
ap-7354	356	16	off	off	ADV
ap-7354	356	17	(	(	PUNCT
ap-7354	356	18	τ	τ	X
ap-7354	356	19	=	=	PROPN
ap-7354	356	20	0	0	NUM
ap-7354	356	21	)	)	PUNCT
ap-7354	356	22	,	,	PUNCT
ap-7354	356	23	where	where	SCONJ
ap-7354	356	24	the	the	DET
ap-7354	356	25	effect	effect	NOUN
ap-7354	356	26	of	of	ADP
ap-7354	356	27	noncommutativity	noncommutativity	NOUN
ap-7354	356	28	is	be	AUX
ap-7354	356	29	very	very	ADV
ap-7354	356	30	significative	significative	ADJ
ap-7354	356	31	as	as	SCONJ
ap-7354	356	32	explained	explain	VERB
ap-7354	356	33	in	in	ADP
ap-7354	356	34	fig	fig	NOUN
ap-7354	356	35	.	.	PUNCT
ap-7354	357	1	1	1	X
ap-7354	357	2	.	.	X
ap-7354	358	1	thereafter	thereafter	ADV
ap-7354	358	2	,	,	PUNCT
ap-7354	358	3	the	the	DET
ap-7354	358	4	effect	effect	NOUN
ap-7354	358	5	of	of	ADP
ap-7354	358	6	noncommutativity	noncommutativity	NOUN
ap-7354	358	7	is	be	AUX
ap-7354	358	8	more	more	ADV
ap-7354	358	9	significative	significative	ADJ
ap-7354	358	10	when	when	SCONJ
ap-7354	358	11	the	the	DET
ap-7354	358	12	dnc	dnc	PROPN
ap-7354	358	13	perturbation	perturbation	NOUN
ap-7354	358	14	term	term	NOUN
ap-7354	358	15	is	be	AUX
ap-7354	358	16	present	present	ADJ
ap-7354	358	17	(	(	PUNCT
ap-7354	358	18	τ	τ	X
ap-7354	358	19	̸=	̸=	PROPN
ap-7354	358	20	0	0	NUM
ap-7354	358	21	)	)	PUNCT
ap-7354	358	22	,	,	PUNCT
ap-7354	358	23	the	the	DET
ap-7354	358	24	presence	presence	NOUN
ap-7354	358	25	of	of	ADP
ap-7354	358	26	this	this	DET
ap-7354	358	27	term	term	NOUN
ap-7354	358	28	exhibits	exhibit	VERB
ap-7354	358	29	the	the	DET
ap-7354	358	30	energy	energy	NOUN
ap-7354	358	31	shifts	shift	NOUN
ap-7354	358	32	.	.	PUNCT
ap-7354	359	1	the	the	DET
ap-7354	359	2	last	last	ADJ
ap-7354	359	3	part	part	NOUN
ap-7354	359	4	of	of	ADP
ap-7354	359	5	fig	fig	NOUN
ap-7354	359	6	.	.	PUNCT
ap-7354	360	1	3	3	NUM
ap-7354	360	2	shows	show	VERB
ap-7354	360	3	the	the	DET
ap-7354	360	4	combined	combined	ADJ
ap-7354	360	5	effect	effect	NOUN
ap-7354	360	6	of	of	ADP
ap-7354	360	7	both	both	CCONJ
ap-7354	360	8	the	the	DET
ap-7354	360	9	dnc	dnc	PROPN
ap-7354	360	10	and	and	CCONJ
ap-7354	360	11	nc	nc	PROPN
ap-7354	360	12	parameters	parameter	NOUN
ap-7354	360	13	,	,	PUNCT
ap-7354	360	14	where	where	SCONJ
ap-7354	360	15	the	the	DET
ap-7354	360	16	effect	effect	NOUN
ap-7354	360	17	is	be	AUX
ap-7354	360	18	very	very	ADV
ap-7354	360	19	evident	evident	ADJ
ap-7354	360	20	.	.	PUNCT
ap-7354	361	1	4	4	X
ap-7354	361	2	.	.	X
ap-7354	361	3	conclusion	conclusion	NOUN
ap-7354	361	4	in	in	ADP
ap-7354	361	5	conclusion	conclusion	NOUN
ap-7354	361	6	,	,	PUNCT
ap-7354	361	7	we	we	PRON
ap-7354	361	8	have	have	AUX
ap-7354	361	9	investigated	investigate	VERB
ap-7354	361	10	the	the	DET
ap-7354	361	11	effects	effect	NOUN
ap-7354	361	12	of	of	ADP
ap-7354	361	13	a	a	DET
ap-7354	361	14	dnc	dnc	PROPN
ap-7354	361	15	space	space	NOUN
ap-7354	361	16	on	on	ADP
ap-7354	361	17	the	the	DET
ap-7354	361	18	2d	2d	NOUN
ap-7354	361	19	do	do	VERB
ap-7354	361	20	in	in	ADP
ap-7354	361	21	the	the	DET
ap-7354	361	22	presence	presence	NOUN
ap-7354	361	23	of	of	ADP
ap-7354	361	24	an	an	DET
ap-7354	361	25	external	external	ADJ
ap-7354	361	26	magnetic	magnetic	ADJ
ap-7354	361	27	field	field	NOUN
ap-7354	361	28	in	in	ADP
ap-7354	361	29	terms	term	NOUN
ap-7354	361	30	of	of	ADP
ap-7354	361	31	creation	creation	NOUN
ap-7354	361	32	and	and	CCONJ
ap-7354	361	33	annihilation	annihilation	NOUN
ap-7354	361	34	operator	operator	NOUN
ap-7354	361	35	languages	language	NOUN
ap-7354	361	36	and	and	CCONJ
ap-7354	361	37	through	through	ADP
ap-7354	361	38	properly	properly	ADV
ap-7354	361	39	chosen	choose	VERB
ap-7354	361	40	canonical	canonical	ADJ
ap-7354	361	41	pairs	pair	NOUN
ap-7354	361	42	of	of	ADP
ap-7354	361	43	coordinates	coordinate	NOUN
ap-7354	361	44	and	and	CCONJ
ap-7354	361	45	its	its	PRON
ap-7354	361	46	corresponding	corresponding	ADJ
ap-7354	361	47	momenta	momenta	NOUN
ap-7354	361	48	in	in	ADP
ap-7354	361	49	a	a	DET
ap-7354	361	50	complex	complex	ADJ
ap-7354	361	51	nc	nc	PROPN
ap-7354	361	52	space	space	NOUN
ap-7354	361	53	.	.	PUNCT
ap-7354	362	1	however	however	ADV
ap-7354	362	2	,	,	PUNCT
ap-7354	362	3	the	the	DET
ap-7354	362	4	dynamical	dynamical	ADJ
ap-7354	362	5	noncommutativity	noncommutativity	NOUN
ap-7354	362	6	was	be	AUX
ap-7354	362	7	treated	treat	VERB
ap-7354	362	8	as	as	ADP
ap-7354	362	9	a	a	DET
ap-7354	362	10	perturbation	perturbation	NOUN
ap-7354	362	11	.	.	PUNCT
ap-7354	363	1	more	more	ADV
ap-7354	363	2	precisely	precisely	ADV
ap-7354	363	3	,	,	PUNCT
ap-7354	363	4	we	we	PRON
ap-7354	363	5	have	have	AUX
ap-7354	363	6	solved	solve	VERB
ap-7354	363	7	the	the	DET
ap-7354	363	8	do	do	NOUN
ap-7354	363	9	problem	problem	NOUN
ap-7354	363	10	in	in	ADP
ap-7354	363	11	a	a	DET
ap-7354	363	12	two	two	NUM
ap-7354	363	13	-	-	PUNCT
ap-7354	363	14	dimensional	dimensional	ADJ
ap-7354	363	15	nc	nc	NOUN
ap-7354	363	16	space	space	NOUN
ap-7354	363	17	to	to	PART
ap-7354	363	18	find	find	VERB
ap-7354	363	19	the	the	DET
ap-7354	363	20	exact	exact	ADJ
ap-7354	363	21	energy	energy	NOUN
ap-7354	363	22	spectrum	spectrum	NOUN
ap-7354	363	23	and	and	CCONJ
ap-7354	363	24	wave	wave	NOUN
ap-7354	363	25	functions	function	NOUN
ap-7354	363	26	.	.	PUNCT
ap-7354	364	1	therefore	therefore	ADV
ap-7354	364	2	,	,	PUNCT
ap-7354	364	3	we	we	PRON
ap-7354	364	4	have	have	AUX
ap-7354	364	5	employed	employ	VERB
ap-7354	364	6	these	these	PRON
ap-7354	364	7	obtained	obtain	VERB
ap-7354	364	8	results	result	NOUN
ap-7354	364	9	to	to	PART
ap-7354	364	10	find	find	VERB
ap-7354	364	11	the	the	DET
ap-7354	364	12	first	first	ADJ
ap-7354	364	13	-	-	PUNCT
ap-7354	364	14	order	order	NOUN
ap-7354	364	15	correction	correction	NOUN
ap-7354	364	16	to	to	ADP
ap-7354	364	17	the	the	DET
ap-7354	364	18	eigenvalues	eigenvalue	NOUN
ap-7354	364	19	and	and	CCONJ
ap-7354	364	20	eigenvectors	eigenvector	NOUN
ap-7354	364	21	.	.	PUNCT
ap-7354	365	1	it	it	PRON
ap-7354	365	2	is	be	AUX
ap-7354	365	3	worth	worth	ADJ
ap-7354	365	4	noting	note	VERB
ap-7354	365	5	that	that	SCONJ
ap-7354	365	6	we	we	PRON
ap-7354	365	7	addressed	address	VERB
ap-7354	365	8	the	the	DET
ap-7354	365	9	system	system	NOUN
ap-7354	365	10	in	in	ADP
ap-7354	365	11	the	the	DET
ap-7354	365	12	nc	nc	PROPN
ap-7354	365	13	space	space	NOUN
ap-7354	365	14	as	as	ADP
ap-7354	365	15	an	an	DET
ap-7354	365	16	unperturbed	unperturbed	ADJ
ap-7354	365	17	system	system	NOUN
ap-7354	365	18	instead	instead	ADV
ap-7354	365	19	of	of	ADP
ap-7354	365	20	considering	consider	VERB
ap-7354	365	21	the	the	DET
ap-7354	365	22	fundamental	fundamental	ADJ
ap-7354	365	23	system	system	NOUN
ap-7354	365	24	in	in	ADP
ap-7354	365	25	a	a	DET
ap-7354	365	26	commutative	commutative	ADJ
ap-7354	365	27	space	space	NOUN
ap-7354	365	28	700	700	NUM
ap-7354	365	29	vol	vol	NOUN
ap-7354	365	30	.	.	PUNCT
ap-7354	366	1	61	61	NUM
ap-7354	366	2	no	no	NOUN
ap-7354	366	3	.	.	PUNCT
ap-7354	367	1	6/2021	6/2021	NUM
ap-7354	367	2	dirac	dirac	NOUN
ap-7354	367	3	oscillator	oscillator	NOUN
ap-7354	367	4	in	in	ADP
ap-7354	367	5	dynamical	dynamical	ADJ
ap-7354	367	6	noncommutative	noncommutative	ADJ
ap-7354	367	7	space	space	NOUN
ap-7354	367	8	and	and	CCONJ
ap-7354	367	9	noncommutativity	noncommutativity	NOUN
ap-7354	367	10	as	as	ADP
ap-7354	367	11	a	a	DET
ap-7354	367	12	perturbation	perturbation	NOUN
ap-7354	367	13	.	.	PUNCT
ap-7354	368	1	the	the	DET
ap-7354	368	2	first	first	ADJ
ap-7354	368	3	-	-	PUNCT
ap-7354	368	4	order	order	NOUN
ap-7354	368	5	correction	correction	NOUN
ap-7354	368	6	for	for	ADP
ap-7354	368	7	the	the	DET
ap-7354	368	8	ground	ground	NOUN
ap-7354	368	9	state	state	NOUN
ap-7354	368	10	of	of	ADP
ap-7354	368	11	the	the	DET
ap-7354	368	12	do	do	NOUN
ap-7354	368	13	due	due	ADP
ap-7354	368	14	to	to	ADP
ap-7354	368	15	the	the	DET
ap-7354	368	16	noncommutativity	noncommutativity	NOUN
ap-7354	368	17	of	of	ADP
ap-7354	368	18	space	space	NOUN
ap-7354	368	19	is	be	AUX
ap-7354	368	20	zero	zero	NUM
ap-7354	368	21	for	for	ADP
ap-7354	368	22	the	the	DET
ap-7354	368	23	non	non	ADJ
ap-7354	368	24	-	-	ADJ
ap-7354	368	25	dnc	dnc	ADJ
ap-7354	368	26	case	case	NOUN
ap-7354	368	27	while	while	SCONJ
ap-7354	368	28	it	it	PRON
ap-7354	368	29	has	have	VERB
ap-7354	368	30	a	a	DET
ap-7354	368	31	nonvanishing	nonvanishe	VERB
ap-7354	368	32	value	value	NOUN
ap-7354	368	33	in	in	ADP
ap-7354	368	34	the	the	DET
ap-7354	368	35	dnc	dnc	PROPN
ap-7354	368	36	case	case	NOUN
ap-7354	368	37	.	.	PUNCT
ap-7354	369	1	knowing	know	VERB
ap-7354	369	2	that	that	SCONJ
ap-7354	369	3	,	,	PUNCT
ap-7354	369	4	the	the	DET
ap-7354	369	5	result	result	NOUN
ap-7354	369	6	reduces	reduce	VERB
ap-7354	369	7	to	to	ADP
ap-7354	369	8	that	that	PRON
ap-7354	369	9	of	of	ADP
ap-7354	369	10	a	a	DET
ap-7354	369	11	usual	usual	ADJ
ap-7354	369	12	do	do	NOUN
ap-7354	369	13	in	in	ADP
ap-7354	369	14	the	the	DET
ap-7354	369	15	limits	limit	NOUN
ap-7354	369	16	of	of	ADP
ap-7354	369	17	τ→0	τ→0	PRON
ap-7354	369	18	,	,	PUNCT
ap-7354	369	19	θ→0	θ→0	PROPN
ap-7354	369	20	.	.	PUNCT
ap-7354	370	1	as	as	SCONJ
ap-7354	370	2	mentioned	mention	VERB
ap-7354	370	3	in	in	ADP
ap-7354	370	4	section	section	NOUN
ap-7354	370	5	2	2	NUM
ap-7354	370	6	,	,	PUNCT
ap-7354	370	7	some	some	DET
ap-7354	370	8	operators	operator	NOUN
ap-7354	370	9	in	in	ADP
ap-7354	370	10	the	the	DET
ap-7354	370	11	dnc	dnc	PROPN
ap-7354	370	12	space	space	NOUN
ap-7354	370	13	are	be	AUX
ap-7354	370	14	non	non	ADJ
ap-7354	370	15	-	-	ADJ
ap-7354	370	16	hermitian	hermitian	ADJ
ap-7354	370	17	.	.	PUNCT
ap-7354	371	1	this	this	DET
ap-7354	371	2	mixture	mixture	NOUN
ap-7354	371	3	of	of	ADP
ap-7354	371	4	dncs	dnc	NOUN
ap-7354	371	5	,	,	PUNCT
ap-7354	371	6	the	the	DET
ap-7354	371	7	non	non	ADJ
ap-7354	371	8	-	-	ADJ
ap-7354	371	9	hermiticity	hermiticity	ADJ
ap-7354	371	10	theory	theory	NOUN
ap-7354	371	11	and	and	CCONJ
ap-7354	371	12	the	the	DET
ap-7354	371	13	string	string	NOUN
ap-7354	371	14	theory	theory	NOUN
ap-7354	371	15	can	can	AUX
ap-7354	371	16	lead	lead	VERB
ap-7354	371	17	to	to	ADP
ap-7354	371	18	fundamental	fundamental	ADJ
ap-7354	371	19	new	new	ADJ
ap-7354	371	20	insights	insight	NOUN
ap-7354	371	21	in	in	ADP
ap-7354	371	22	these	these	DET
ap-7354	371	23	three	three	NUM
ap-7354	371	24	fields	field	NOUN
ap-7354	371	25	.	.	PUNCT
ap-7354	372	1	distinctly	distinctly	ADV
ap-7354	372	2	,	,	PUNCT
ap-7354	372	3	there	there	PRON
ap-7354	372	4	are	be	VERB
ap-7354	372	5	plenty	plenty	NOUN
ap-7354	372	6	of	of	ADP
ap-7354	372	7	interesting	interesting	ADJ
ap-7354	372	8	problems	problem	NOUN
ap-7354	372	9	arising	arise	VERB
ap-7354	372	10	from	from	ADP
ap-7354	372	11	our	our	PRON
ap-7354	372	12	investigation	investigation	NOUN
ap-7354	372	13	,	,	PUNCT
ap-7354	372	14	such	such	ADJ
ap-7354	372	15	as	as	ADP
ap-7354	372	16	the	the	DET
ap-7354	372	17	investigation	investigation	NOUN
ap-7354	372	18	of	of	ADP
ap-7354	372	19	further	further	ADJ
ap-7354	372	20	possibilities	possibility	NOUN
ap-7354	372	21	of	of	ADP
ap-7354	372	22	consistent	consistent	ADJ
ap-7354	372	23	deformations	deformation	NOUN
ap-7354	372	24	,	,	PUNCT
ap-7354	372	25	and	and	CCONJ
ap-7354	372	26	studies	study	NOUN
ap-7354	372	27	of	of	ADP
ap-7354	372	28	additional	additional	ADJ
ap-7354	372	29	models	model	NOUN
ap-7354	372	30	in	in	ADP
ap-7354	372	31	terms	term	NOUN
ap-7354	372	32	of	of	ADP
ap-7354	372	33	the	the	DET
ap-7354	372	34	dnc	dnc	PROPN
ap-7354	372	35	variables	variable	NOUN
ap-7354	372	36	.	.	PUNCT
ap-7354	373	1	references	reference	NOUN
ap-7354	373	2	[	[	X
ap-7354	373	3	1	1	NUM
ap-7354	373	4	]	]	X
ap-7354	373	5	n.	n.	PROPN
ap-7354	373	6	seiberg	seiberg	PROPN
ap-7354	373	7	,	,	PUNCT
ap-7354	373	8	e.	e.	PROPN
ap-7354	373	9	witten	witten	PROPN
ap-7354	373	10	.	.	PUNCT
ap-7354	374	1	string	string	PROPN
ap-7354	374	2	theory	theory	NOUN
ap-7354	374	3	and	and	CCONJ
ap-7354	374	4	noncommutative	noncommutative	ADJ
ap-7354	374	5	geometry	geometry	NOUN
ap-7354	374	6	.	.	PUNCT
ap-7354	375	1	journal	journal	PROPN
ap-7354	375	2	of	of	ADP
ap-7354	375	3	high	high	ADJ
ap-7354	375	4	energy	energy	NOUN
ap-7354	375	5	physics	physics	NOUN
ap-7354	375	6	(	(	PUNCT
ap-7354	375	7	9):032	9):032	NOUN
ap-7354	375	8	,	,	PUNCT
ap-7354	375	9	1999	1999	NUM
ap-7354	375	10	.	.	PUNCT
ap-7354	376	1	https://doi.org/10.1088/1126-6708/1999/09/032	https://doi.org/10.1088/1126-6708/1999/09/032	PROPN
ap-7354	376	2	.	.	PUNCT
ap-7354	377	1	[	[	X
ap-7354	377	2	2	2	NUM
ap-7354	377	3	]	]	PUNCT
ap-7354	377	4	d.	d.	PROPN
ap-7354	377	5	m.	m.	PROPN
ap-7354	377	6	gingrich	gingrich	PROPN
ap-7354	377	7	.	.	PUNCT
ap-7354	378	1	noncommutative	noncommutative	ADJ
ap-7354	378	2	geometry	geometry	NOUN
ap-7354	378	3	inspired	inspire	VERB
ap-7354	378	4	blackholes	blackhole	NOUN
ap-7354	378	5	in	in	ADP
ap-7354	378	6	higher	high	ADJ
ap-7354	378	7	dimensions	dimension	NOUN
ap-7354	378	8	at	at	ADP
ap-7354	378	9	the	the	DET
ap-7354	378	10	lhc	lhc	PROPN
ap-7354	378	11	.	.	PUNCT
ap-7354	379	1	journal	journal	PROPN
ap-7354	379	2	of	of	ADP
ap-7354	379	3	high	high	ADJ
ap-7354	379	4	energy	energy	NOUN
ap-7354	379	5	physics	physics	NOUN
ap-7354	379	6	2010:22	2010:22	NUM
ap-7354	379	7	,	,	PUNCT
ap-7354	379	8	2010	2010	NUM
ap-7354	379	9	.	.	PUNCT
ap-7354	380	1	https://doi.org/10.1007/jhep05(2010)022	https://doi.org/10.1007/jhep05(2010)022	NOUN
ap-7354	380	2	.	.	PUNCT
ap-7354	381	1	[	[	X
ap-7354	381	2	3	3	X
ap-7354	381	3	]	]	X
ap-7354	381	4	p.	p.	PROPN
ap-7354	381	5	nicolini	nicolini	PROPN
ap-7354	381	6	.	.	PUNCT
ap-7354	381	7	noncommutative	noncommutative	ADJ
ap-7354	381	8	black	black	ADJ
ap-7354	381	9	holes	hole	NOUN
ap-7354	381	10	,	,	PUNCT
ap-7354	381	11	the	the	DET
ap-7354	381	12	final	final	ADJ
ap-7354	381	13	appeal	appeal	NOUN
ap-7354	381	14	to	to	ADP
ap-7354	381	15	quantum	quantum	ADJ
ap-7354	381	16	gravity	gravity	NOUN
ap-7354	381	17	:	:	PUNCT
ap-7354	381	18	a	a	DET
ap-7354	381	19	review	review	NOUN
ap-7354	381	20	.	.	PUNCT
ap-7354	382	1	international	international	ADJ
ap-7354	382	2	journal	journal	PROPN
ap-7354	382	3	of	of	ADP
ap-7354	382	4	modern	modern	ADJ
ap-7354	382	5	physics	physic	NOUN
ap-7354	382	6	a	a	DET
ap-7354	382	7	24(7):1229–1308	24(7):1229–1308	PROPN
ap-7354	382	8	,	,	PUNCT
ap-7354	382	9	2009	2009	NUM
ap-7354	382	10	.	.	PUNCT
ap-7354	383	1	https://doi.org/10.1142/s0217751x09043353	https://doi.org/10.1142/s0217751x09043353	X
ap-7354	383	2	.	.	PUNCT
ap-7354	384	1	[	[	X
ap-7354	384	2	4	4	X
ap-7354	384	3	]	]	PUNCT
ap-7354	384	4	j.	j.	PROPN
ap-7354	384	5	m.	m.	PROPN
ap-7354	384	6	gracia	gracia	PROPN
ap-7354	384	7	-	-	PUNCT
ap-7354	384	8	bondia	bondia	NOUN
ap-7354	384	9	.	.	PUNCT
ap-7354	385	1	new	new	ADJ
ap-7354	385	2	paths	path	NOUN
ap-7354	385	3	towards	towards	ADP
ap-7354	385	4	quantum	quantum	ADJ
ap-7354	385	5	gravity	gravity	NOUN
ap-7354	385	6	,	,	PUNCT
ap-7354	385	7	chap	chap	PROPN
ap-7354	385	8	.	.	PUNCT
ap-7354	386	1	notes	note	NOUN
ap-7354	386	2	on	on	ADP
ap-7354	386	3	quantum	quantum	NOUN
ap-7354	386	4	gravity	gravity	NOUN
ap-7354	386	5	and	and	CCONJ
ap-7354	386	6	noncommutative	noncommutative	ADJ
ap-7354	386	7	geometry	geometry	NOUN
ap-7354	386	8	,	,	PUNCT
ap-7354	386	9	pp	pp	ADP
ap-7354	386	10	.	.	PUNCT
ap-7354	387	1	3–58	3–58	PROPN
ap-7354	387	2	.	.	PUNCT
ap-7354	387	3	springer	springer	PROPN
ap-7354	387	4	,	,	PUNCT
ap-7354	387	5	berlin	berlin	PROPN
ap-7354	387	6	,	,	PUNCT
ap-7354	387	7	heidelberg	heidelberg	PROPN
ap-7354	387	8	,	,	PUNCT
ap-7354	387	9	2010	2010	NUM
ap-7354	387	10	.	.	PUNCT
ap-7354	388	1	https://doi.org/10.1007/978-3-642-11897-5_1	https://doi.org/10.1007/978-3-642-11897-5_1	X
ap-7354	388	2	.	.	PUNCT
ap-7354	389	1	[	[	X
ap-7354	389	2	5	5	NUM
ap-7354	389	3	]	]	PUNCT
ap-7354	389	4	m.	m.	NOUN
ap-7354	389	5	chaichian	chaichian	PROPN
ap-7354	389	6	,	,	PUNCT
ap-7354	389	7	m.	m.	NOUN
ap-7354	389	8	m.	m.	NOUN
ap-7354	389	9	sheikh	sheikh	PROPN
ap-7354	389	10	-	-	PUNCT
ap-7354	389	11	jabbari	jabbari	NOUN
ap-7354	389	12	,	,	PUNCT
ap-7354	389	13	a.	a.	NOUN
ap-7354	389	14	tureanu	tureanu	NOUN
ap-7354	389	15	.	.	PUNCT
ap-7354	390	1	hydrogen	hydrogen	NOUN
ap-7354	390	2	atom	atom	NOUN
ap-7354	390	3	spectrum	spectrum	NOUN
ap-7354	390	4	and	and	CCONJ
ap-7354	390	5	the	the	DET
ap-7354	390	6	lamb	lamb	PROPN
ap-7354	390	7	shift	shift	NOUN
ap-7354	390	8	in	in	ADP
ap-7354	390	9	noncommutative	noncommutative	PROPN
ap-7354	390	10	qed	qed	PROPN
ap-7354	390	11	.	.	PUNCT
ap-7354	391	1	physical	physical	PROPN
ap-7354	391	2	review	review	NOUN
ap-7354	391	3	letters	letter	NOUN
ap-7354	391	4	86(13):2716–2719	86(13):2716–2719	NUM
ap-7354	391	5	,	,	PUNCT
ap-7354	391	6	2001	2001	NUM
ap-7354	391	7	.	.	PUNCT
ap-7354	392	1	https://doi.org/10.1103/physrevlett.86.2716	https://doi.org/10.1103/physrevlett.86.2716	NOUN
ap-7354	392	2	.	.	PUNCT
ap-7354	393	1	[	[	X
ap-7354	393	2	6	6	NUM
ap-7354	393	3	]	]	X
ap-7354	393	4	i.	i.	PROPN
ap-7354	393	5	haouam	haouam	PROPN
ap-7354	393	6	.	.	PUNCT
ap-7354	394	1	analytical	analytical	ADJ
ap-7354	394	2	solution	solution	NOUN
ap-7354	394	3	of	of	ADP
ap-7354	394	4	(	(	PUNCT
ap-7354	394	5	2	2	NUM
ap-7354	394	6	+	+	NOUN
ap-7354	394	7	1	1	NUM
ap-7354	394	8	)	)	PUNCT
ap-7354	394	9	dimensional	dimensional	ADJ
ap-7354	394	10	dirac	dirac	NOUN
ap-7354	394	11	equation	equation	NOUN
ap-7354	394	12	in	in	ADP
ap-7354	394	13	time	time	NOUN
ap-7354	394	14	-	-	PUNCT
ap-7354	394	15	dependent	dependent	ADJ
ap-7354	394	16	noncommutative	noncommutative	ADJ
ap-7354	394	17	phase	phase	NOUN
ap-7354	394	18	-	-	PUNCT
ap-7354	394	19	space	space	NOUN
ap-7354	394	20	.	.	PUNCT
ap-7354	395	1	acta	acta	PROPN
ap-7354	395	2	polytechnica	polytechnica	PROPN
ap-7354	395	3	60(2):111–121	60(2):111–121	PROPN
ap-7354	395	4	,	,	PUNCT
ap-7354	395	5	2020	2020	NUM
ap-7354	395	6	.	.	PUNCT
ap-7354	396	1	https://doi.org/10.14311/ap.2020.60.0111	https://doi.org/10.14311/ap.2020.60.0111	X
ap-7354	396	2	.	.	PUNCT
ap-7354	397	1	[	[	X
ap-7354	397	2	7	7	NUM
ap-7354	397	3	]	]	X
ap-7354	397	4	i.	i.	PROPN
ap-7354	397	5	haouam	haouam	PROPN
ap-7354	397	6	.	.	PUNCT
ap-7354	398	1	on	on	ADP
ap-7354	398	2	the	the	DET
ap-7354	398	3	noncommutative	noncommutative	ADJ
ap-7354	398	4	geometry	geometry	NOUN
ap-7354	398	5	in	in	ADP
ap-7354	398	6	quantum	quantum	ADJ
ap-7354	398	7	mechanics	mechanic	NOUN
ap-7354	398	8	.	.	PUNCT
ap-7354	399	1	journal	journal	PROPN
ap-7354	399	2	of	of	ADP
ap-7354	399	3	physical	physical	ADJ
ap-7354	399	4	studies	study	NOUN
ap-7354	399	5	24(2):1–10	24(2):1–10	NUM
ap-7354	399	6	,	,	PUNCT
ap-7354	399	7	2002	2002	NUM
ap-7354	399	8	.	.	PUNCT
ap-7354	400	1	https://doi.org/10.30970/jps.24.2002	https://doi.org/10.30970/jps.24.2002	NOUN
ap-7354	400	2	.	.	PUNCT
ap-7354	401	1	[	[	X
ap-7354	401	2	8	8	NUM
ap-7354	401	3	]	]	PUNCT
ap-7354	401	4	m.	m.	PROPN
ap-7354	401	5	r.	r.	PROPN
ap-7354	401	6	douglas	douglas	PROPN
ap-7354	401	7	,	,	PUNCT
ap-7354	401	8	n.	n.	NOUN
ap-7354	401	9	a.	a.	NOUN
ap-7354	401	10	nekrasov	nekrasov	NOUN
ap-7354	401	11	.	.	PUNCT
ap-7354	402	1	noncommutative	noncommutative	ADJ
ap-7354	402	2	field	field	PROPN
ap-7354	402	3	theory	theory	NOUN
ap-7354	402	4	.	.	PUNCT
ap-7354	403	1	reviews	review	NOUN
ap-7354	403	2	of	of	ADP
ap-7354	403	3	modern	modern	ADJ
ap-7354	403	4	physics	physics	NOUN
ap-7354	403	5	73(4):977–1029	73(4):977–1029	PROPN
ap-7354	403	6	,	,	PUNCT
ap-7354	403	7	2001	2001	NUM
ap-7354	403	8	.	.	PUNCT
ap-7354	404	1	https://doi.org/10.1103/revmodphys.73.977	https://doi.org/10.1103/revmodphys.73.977	PROPN
ap-7354	404	2	.	.	PUNCT
ap-7354	405	1	[	[	X
ap-7354	405	2	9	9	NUM
ap-7354	405	3	]	]	SYM
ap-7354	405	4	i.	i.	PROPN
ap-7354	405	5	haouam	haouam	PROPN
ap-7354	405	6	.	.	PUNCT
ap-7354	406	1	on	on	ADP
ap-7354	406	2	the	the	DET
ap-7354	406	3	fisk	fisk	PROPN
ap-7354	406	4	-	-	PUNCT
ap-7354	406	5	tait	tait	PROPN
ap-7354	406	6	equation	equation	NOUN
ap-7354	406	7	for	for	ADP
ap-7354	406	8	spin-3/2	spin-3/2	NOUN
ap-7354	406	9	fermions	fermion	NOUN
ap-7354	406	10	interacting	interact	VERB
ap-7354	406	11	with	with	ADP
ap-7354	406	12	an	an	DET
ap-7354	406	13	external	external	ADJ
ap-7354	406	14	magnetic	magnetic	ADJ
ap-7354	406	15	field	field	NOUN
ap-7354	406	16	in	in	ADP
ap-7354	406	17	noncommutative	noncommutative	ADJ
ap-7354	406	18	space	space	NOUN
ap-7354	406	19	-	-	PUNCT
ap-7354	406	20	time	time	NOUN
ap-7354	406	21	.	.	PUNCT
ap-7354	407	1	journal	journal	PROPN
ap-7354	407	2	of	of	ADP
ap-7354	407	3	physical	physical	ADJ
ap-7354	407	4	studies	study	NOUN
ap-7354	407	5	24(1):1801	24(1):1801	NUM
ap-7354	407	6	,	,	PUNCT
ap-7354	407	7	2020	2020	NUM
ap-7354	407	8	.	.	PUNCT
ap-7354	408	1	https://doi.org/10.30970/jps.24.1801	https://doi.org/10.30970/jps.24.1801	X
ap-7354	408	2	.	.	PUNCT
ap-7354	409	1	[	[	X
ap-7354	409	2	10	10	NUM
ap-7354	409	3	]	]	X
ap-7354	409	4	h.	h.	PROPN
ap-7354	409	5	s.	s.	PROPN
ap-7354	409	6	snyder	snyder	PROPN
ap-7354	409	7	.	.	PUNCT
ap-7354	410	1	quantized	quantize	VERB
ap-7354	410	2	space	space	NOUN
ap-7354	410	3	-	-	PUNCT
ap-7354	410	4	time	time	NOUN
ap-7354	410	5	.	.	PUNCT
ap-7354	411	1	physical	physical	ADJ
ap-7354	411	2	review	review	NOUN
ap-7354	411	3	71(1):38–41	71(1):38–41	NUM
ap-7354	411	4	,	,	PUNCT
ap-7354	411	5	1947	1947	NUM
ap-7354	411	6	.	.	PUNCT
ap-7354	412	1	https://doi.org/10.1103/physrev.71.38	https://doi.org/10.1103/physrev.71.38	NOUN
ap-7354	412	2	.	.	PUNCT
ap-7354	413	1	[	[	X
ap-7354	413	2	11	11	NUM
ap-7354	413	3	]	]	PUNCT
ap-7354	413	4	h.	h.	PROPN
ap-7354	413	5	s.	s.	PROPN
ap-7354	413	6	snyder	snyder	PROPN
ap-7354	413	7	.	.	PUNCT
ap-7354	414	1	the	the	DET
ap-7354	414	2	electromagnetic	electromagnetic	ADJ
ap-7354	414	3	field	field	NOUN
ap-7354	414	4	in	in	ADP
ap-7354	414	5	quantized	quantize	VERB
ap-7354	414	6	space	space	NOUN
ap-7354	414	7	-	-	PUNCT
ap-7354	414	8	time	time	NOUN
ap-7354	414	9	.	.	PUNCT
ap-7354	415	1	physical	physical	ADJ
ap-7354	415	2	review	review	NOUN
ap-7354	415	3	72(1):68–71	72(1):68–71	NUM
ap-7354	415	4	,	,	PUNCT
ap-7354	415	5	1947	1947	NUM
ap-7354	415	6	.	.	PUNCT
ap-7354	416	1	https://doi.org/10.1103/physrev.72.68	https://doi.org/10.1103/physrev.72.68	NOUN
ap-7354	416	2	.	.	PUNCT
ap-7354	417	1	[	[	X
ap-7354	417	2	12	12	NUM
ap-7354	417	3	]	]	X
ap-7354	417	4	n.	n.	NOUN
ap-7354	417	5	sasakura	sasakura	NOUN
ap-7354	417	6	.	.	PUNCT
ap-7354	418	1	space	space	NOUN
ap-7354	418	2	-	-	PUNCT
ap-7354	418	3	time	time	NOUN
ap-7354	418	4	uncertainty	uncertainty	NOUN
ap-7354	418	5	relation	relation	NOUN
ap-7354	418	6	and	and	CCONJ
ap-7354	418	7	lorentz	lorentz	PROPN
ap-7354	418	8	invariance	invariance	NOUN
ap-7354	418	9	.	.	PUNCT
ap-7354	419	1	journal	journal	NOUN
ap-7354	419	2	of	of	ADP
ap-7354	419	3	high	high	ADJ
ap-7354	419	4	energy	energy	NOUN
ap-7354	419	5	physics	physics	NOUN
ap-7354	419	6	(	(	PUNCT
ap-7354	419	7	05):015	05):015	NOUN
ap-7354	419	8	,	,	PUNCT
ap-7354	419	9	2000	2000	NUM
ap-7354	419	10	.	.	PUNCT
ap-7354	420	1	https://doi.org/10.1088/1126-6708/2000/05/015	https://doi.org/10.1088/1126-6708/2000/05/015	PROPN
ap-7354	420	2	.	.	PUNCT
ap-7354	421	1	[	[	X
ap-7354	421	2	13	13	NUM
ap-7354	421	3	]	]	PUNCT
ap-7354	421	4	j.	j.	PROPN
ap-7354	421	5	lukierski	lukierski	PROPN
ap-7354	421	6	,	,	PUNCT
ap-7354	421	7	h.	h.	PROPN
ap-7354	421	8	ruegg	ruegg	NOUN
ap-7354	421	9	,	,	PUNCT
ap-7354	421	10	a.	a.	PROPN
ap-7354	421	11	nowicki	nowicki	PROPN
ap-7354	421	12	,	,	PUNCT
ap-7354	421	13	v.	v.	ADP
ap-7354	421	14	n.	n.	PROPN
ap-7354	421	15	tolstoi	tolstoi	NOUN
ap-7354	421	16	.	.	PUNCT
ap-7354	422	1	q	q	X
ap-7354	422	2	-	-	PUNCT
ap-7354	422	3	deformation	deformation	NOUN
ap-7354	422	4	of	of	ADP
ap-7354	422	5	poincaré	poincaré	PROPN
ap-7354	422	6	algebra	algebra	PROPN
ap-7354	422	7	.	.	PUNCT
ap-7354	423	1	physics	physics	NOUN
ap-7354	423	2	letters	letter	NOUN
ap-7354	423	3	b	b	PROPN
ap-7354	423	4	264(3	264(3	NUM
ap-7354	423	5	-	-	SYM
ap-7354	423	6	4):331–338	4):331–338	NUM
ap-7354	423	7	,	,	PUNCT
ap-7354	423	8	1991	1991	NUM
ap-7354	423	9	.	.	PUNCT
ap-7354	424	1	https://doi.org/10.1016/0370-2693(91)90358-w	https://doi.org/10.1016/0370-2693(91)90358-w	NOUN
ap-7354	424	2	.	.	PUNCT
ap-7354	425	1	[	[	X
ap-7354	425	2	14	14	NUM
ap-7354	425	3	]	]	PUNCT
ap-7354	425	4	a.	a.	NOUN
ap-7354	425	5	p.	p.	PROPN
ap-7354	425	6	balachandran	balachandran	PROPN
ap-7354	425	7	,	,	PUNCT
ap-7354	425	8	s.	s.	PROPN
ap-7354	425	9	vaidya	vaidya	PROPN
ap-7354	425	10	.	.	PUNCT
ap-7354	425	11	lectures	lecture	VERB
ap-7354	425	12	on	on	ADP
ap-7354	425	13	fuzzy	fuzzy	ADJ
ap-7354	425	14	and	and	CCONJ
ap-7354	425	15	fuzzy	fuzzy	ADJ
ap-7354	425	16	susy	susy	NOUN
ap-7354	425	17	physics	physics	PROPN
ap-7354	425	18	,	,	PUNCT
ap-7354	425	19	2007	2007	NUM
ap-7354	425	20	.	.	PUNCT
ap-7354	426	1	world	world	NOUN
ap-7354	426	2	scientific	scientific	ADJ
ap-7354	426	3	.	.	PUNCT
ap-7354	427	1	iisc	iisc	PROPN
ap-7354	427	2	/	/	SYM
ap-7354	427	3	chep/11/05	chep/11/05	PROPN
ap-7354	427	4	.	.	PUNCT
ap-7354	428	1	[	[	X
ap-7354	428	2	15	15	NUM
ap-7354	428	3	]	]	X
ap-7354	428	4	s.	s.	PROPN
ap-7354	428	5	a.	a.	PROPN
ap-7354	428	6	alavi	alavi	PROPN
ap-7354	428	7	,	,	PUNCT
ap-7354	428	8	n.	n.	PROPN
ap-7354	428	9	rezaei	rezaei	PROPN
ap-7354	428	10	.	.	PUNCT
ap-7354	428	11	dirac	dirac	PROPN
ap-7354	428	12	equation	equation	NOUN
ap-7354	428	13	,	,	PUNCT
ap-7354	428	14	hydrogen	hydrogen	NOUN
ap-7354	428	15	atom	atom	NOUN
ap-7354	428	16	spectrum	spectrum	NOUN
ap-7354	428	17	and	and	CCONJ
ap-7354	428	18	the	the	DET
ap-7354	428	19	lamb	lamb	PROPN
ap-7354	428	20	shift	shift	NOUN
ap-7354	428	21	in	in	ADP
ap-7354	428	22	dynamical	dynamical	ADJ
ap-7354	428	23	non	non	ADJ
ap-7354	428	24	-	-	ADJ
ap-7354	428	25	commutative	commutative	ADJ
ap-7354	428	26	spaces	space	NOUN
ap-7354	428	27	.	.	PUNCT
ap-7354	429	1	pramana	pramana	PROPN
ap-7354	429	2	88:77	88:77	NUM
ap-7354	429	3	,	,	PUNCT
ap-7354	429	4	2017	2017	NUM
ap-7354	429	5	.	.	PUNCT
ap-7354	430	1	https://doi.org/10.1007/s12043-017-1381-4	https://doi.org/10.1007/s12043-017-1381-4	NUM
ap-7354	430	2	.	.	PUNCT
ap-7354	431	1	[	[	X
ap-7354	431	2	16	16	NUM
ap-7354	431	3	]	]	X
ap-7354	431	4	a.	a.	NOUN
ap-7354	431	5	fring	fring	PROPN
ap-7354	431	6	,	,	PUNCT
ap-7354	431	7	l.	l.	PROPN
ap-7354	431	8	gouba	gouba	PROPN
ap-7354	431	9	,	,	PUNCT
ap-7354	431	10	f.	f.	PROPN
ap-7354	431	11	g.	g.	PROPN
ap-7354	431	12	scholtz	scholtz	PROPN
ap-7354	431	13	.	.	PUNCT
ap-7354	432	1	strings	string	NOUN
ap-7354	432	2	from	from	ADP
ap-7354	432	3	position	position	NOUN
ap-7354	432	4	-	-	PUNCT
ap-7354	432	5	dependent	dependent	ADJ
ap-7354	432	6	noncommutativity	noncommutativity	NOUN
ap-7354	432	7	.	.	PUNCT
ap-7354	433	1	journal	journal	PROPN
ap-7354	433	2	of	of	ADP
ap-7354	433	3	physics	physics	PROPN
ap-7354	433	4	a	a	PRON
ap-7354	433	5	:	:	PUNCT
ap-7354	433	6	mathematical	mathematical	ADJ
ap-7354	433	7	and	and	CCONJ
ap-7354	433	8	theoretical	theoretical	ADJ
ap-7354	433	9	43:345401	43:345401	NUM
ap-7354	433	10	,	,	PUNCT
ap-7354	433	11	2010	2010	NUM
ap-7354	433	12	.	.	PUNCT
ap-7354	434	1	https://doi.org/10.1088/1751-8113/43/34/345401	https://doi.org/10.1088/1751-8113/43/34/345401	NOUN
ap-7354	434	2	.	.	PUNCT
ap-7354	435	1	[	[	X
ap-7354	435	2	17	17	NUM
ap-7354	435	3	]	]	PUNCT
ap-7354	435	4	m.	m.	NOUN
ap-7354	435	5	gomes	gome	NOUN
ap-7354	435	6	,	,	PUNCT
ap-7354	435	7	v.	v.	PROPN
ap-7354	435	8	g.	g.	PROPN
ap-7354	435	9	kupriyanov	kupriyanov	PROPN
ap-7354	435	10	.	.	PUNCT
ap-7354	436	1	position	position	NOUN
ap-7354	436	2	-	-	PUNCT
ap-7354	436	3	dependent	dependent	ADJ
ap-7354	436	4	noncommutativity	noncommutativity	NOUN
ap-7354	436	5	in	in	ADP
ap-7354	436	6	quantum	quantum	ADJ
ap-7354	436	7	mechanics	mechanic	NOUN
ap-7354	436	8	.	.	PUNCT
ap-7354	437	1	physical	physical	ADJ
ap-7354	437	2	review	review	PROPN
ap-7354	437	3	d	d	PROPN
ap-7354	437	4	79:125011	79:125011	NOUN
ap-7354	437	5	,	,	PUNCT
ap-7354	437	6	2009	2009	NUM
ap-7354	437	7	.	.	PUNCT
ap-7354	438	1	https://doi.org/10.1103/physrevd.79.125011	https://doi.org/10.1103/physrevd.79.125011	PROPN
ap-7354	438	2	.	.	PUNCT
ap-7354	439	1	[	[	X
ap-7354	439	2	18	18	NUM
ap-7354	439	3	]	]	X
ap-7354	439	4	d.	d.	PROPN
ap-7354	439	5	itô	itô	PROPN
ap-7354	439	6	,	,	PUNCT
ap-7354	439	7	k.	k.	PROPN
ap-7354	439	8	mori	mori	PROPN
ap-7354	439	9	,	,	PUNCT
ap-7354	439	10	e.	e.	PROPN
ap-7354	439	11	carriere	carriere	PROPN
ap-7354	439	12	.	.	PUNCT
ap-7354	440	1	an	an	DET
ap-7354	440	2	example	example	NOUN
ap-7354	440	3	of	of	ADP
ap-7354	440	4	dynamical	dynamical	ADJ
ap-7354	440	5	systems	system	NOUN
ap-7354	440	6	with	with	ADP
ap-7354	440	7	linear	linear	PROPN
ap-7354	440	8	trajectory	trajectory	NOUN
ap-7354	440	9	.	.	PUNCT
ap-7354	441	1	nuovo	nuovo	PROPN
ap-7354	441	2	cimento	cimento	PROPN
ap-7354	441	3	a	a	PRON
ap-7354	441	4	(	(	PUNCT
ap-7354	441	5	1965	1965	NUM
ap-7354	441	6	-	-	SYM
ap-7354	441	7	1970	1970	NUM
ap-7354	441	8	)	)	PUNCT
ap-7354	441	9	51:1119–1121	51:1119–1121	NUM
ap-7354	441	10	,	,	PUNCT
ap-7354	441	11	1967	1967	NUM
ap-7354	441	12	.	.	PUNCT
ap-7354	442	1	https://doi.org/10.1007/bf02721775	https://doi.org/10.1007/bf02721775	PROPN
ap-7354	442	2	.	.	PUNCT
ap-7354	443	1	[	[	X
ap-7354	443	2	19	19	NUM
ap-7354	443	3	]	]	PUNCT
ap-7354	443	4	m.	m.	NOUN
ap-7354	443	5	moshinsky	moshinsky	PROPN
ap-7354	443	6	,	,	PUNCT
ap-7354	443	7	a.	a.	NOUN
ap-7354	443	8	szczepaniak	szczepaniak	NOUN
ap-7354	443	9	.	.	PUNCT
ap-7354	444	1	the	the	DET
ap-7354	444	2	dirac	dirac	PROPN
ap-7354	444	3	oscillator	oscillator	PROPN
ap-7354	444	4	.	.	PUNCT
ap-7354	445	1	journal	journal	PROPN
ap-7354	445	2	of	of	ADP
ap-7354	445	3	physics	physics	PROPN
ap-7354	445	4	a	a	PRON
ap-7354	445	5	:	:	PUNCT
ap-7354	445	6	mathematical	mathematical	ADJ
ap-7354	445	7	and	and	CCONJ
ap-7354	445	8	general	general	ADJ
ap-7354	445	9	22(17):l817	22(17):l817	NUM
ap-7354	445	10	,	,	PUNCT
ap-7354	445	11	1989	1989	NUM
ap-7354	445	12	.	.	PUNCT
ap-7354	446	1	https://doi.org/10.1088/0305-4470/22/17/002	https://doi.org/10.1088/0305-4470/22/17/002	NOUN
ap-7354	446	2	.	.	PUNCT
ap-7354	447	1	[	[	X
ap-7354	447	2	20	20	NUM
ap-7354	447	3	]	]	PUNCT
ap-7354	447	4	r.	r.	PROPN
ap-7354	447	5	p.	p.	PROPN
ap-7354	447	6	martínez	martínez	PROPN
ap-7354	447	7	-	-	PUNCT
ap-7354	447	8	y	y	PROPN
ap-7354	447	9	-	-	PUNCT
ap-7354	447	10	romero	romero	PROPN
ap-7354	447	11	,	,	PUNCT
ap-7354	447	12	a.	a.	PROPN
ap-7354	447	13	l.	l.	PROPN
ap-7354	447	14	salas	salas	PROPN
ap-7354	447	15	-	-	PUNCT
ap-7354	447	16	brito	brito	PROPN
ap-7354	447	17	.	.	PUNCT
ap-7354	447	18	conformal	conformal	ADJ
ap-7354	447	19	invariance	invariance	NOUN
ap-7354	447	20	in	in	ADP
ap-7354	447	21	a	a	DET
ap-7354	447	22	dirac	dirac	NOUN
ap-7354	447	23	oscillator	oscillator	NOUN
ap-7354	447	24	.	.	PUNCT
ap-7354	448	1	journal	journal	PROPN
ap-7354	448	2	of	of	ADP
ap-7354	448	3	mathematical	mathematical	ADJ
ap-7354	448	4	physics	physics	NOUN
ap-7354	448	5	33(5):1831	33(5):1831	NUM
ap-7354	448	6	,	,	PUNCT
ap-7354	448	7	1992	1992	NUM
ap-7354	448	8	.	.	PUNCT
ap-7354	449	1	https://doi.org/10.1063/1.529660	https://doi.org/10.1063/1.529660	PROPN
ap-7354	449	2	.	.	PUNCT
ap-7354	450	1	[	[	X
ap-7354	450	2	21	21	NUM
ap-7354	450	3	]	]	PUNCT
ap-7354	450	4	j.	j.	PROPN
ap-7354	450	5	benitez	benitez	PROPN
ap-7354	450	6	,	,	PUNCT
ap-7354	450	7	p.	p.	PROPN
ap-7354	450	8	r.	r.	PROPN
ap-7354	450	9	martnez	martnez	PROPN
ap-7354	450	10	y	y	PROPN
ap-7354	450	11	romero	romero	PROPN
ap-7354	450	12	,	,	PUNCT
ap-7354	450	13	h.	h.	PROPN
ap-7354	450	14	n.	n.	PROPN
ap-7354	450	15	núnez	núnez	PROPN
ap-7354	450	16	-	-	PUNCT
ap-7354	450	17	yépez	yépez	PROPN
ap-7354	450	18	,	,	PUNCT
ap-7354	450	19	a.	a.	PROPN
ap-7354	450	20	l.	l.	PROPN
ap-7354	450	21	salas	salas	PROPN
ap-7354	450	22	-	-	PUNCT
ap-7354	450	23	brito	brito	PROPN
ap-7354	450	24	.	.	PUNCT
ap-7354	450	25	solution	solution	NOUN
ap-7354	450	26	and	and	CCONJ
ap-7354	450	27	hidden	hide	VERB
ap-7354	450	28	supersymmetry	supersymmetry	NOUN
ap-7354	450	29	of	of	ADP
ap-7354	450	30	a	a	DET
ap-7354	450	31	dirac	dirac	NOUN
ap-7354	450	32	oscillator	oscillator	NOUN
ap-7354	450	33	.	.	PUNCT
ap-7354	451	1	physical	physical	PROPN
ap-7354	451	2	review	review	NOUN
ap-7354	451	3	letters	letter	NOUN
ap-7354	451	4	64:1643	64:1643	NOUN
ap-7354	451	5	,	,	PUNCT
ap-7354	451	6	1990	1990	NUM
ap-7354	451	7	.	.	PUNCT
ap-7354	452	1	https://doi.org/10.1103/physrevlett.64.1643	https://doi.org/10.1103/physrevlett.64.1643	NOUN
ap-7354	452	2	.	.	PUNCT
ap-7354	453	1	[	[	X
ap-7354	453	2	22	22	NUM
ap-7354	453	3	]	]	PUNCT
ap-7354	453	4	c.	c.	NOUN
ap-7354	453	5	quesne	quesne	NOUN
ap-7354	453	6	,	,	PUNCT
ap-7354	453	7	m.	m.	NOUN
ap-7354	453	8	moshinsky	moshinsky	PROPN
ap-7354	453	9	.	.	PUNCT
ap-7354	454	1	symmetry	symmetry	NOUN
ap-7354	454	2	lie	lie	NOUN
ap-7354	454	3	algebra	algebra	NOUN
ap-7354	454	4	of	of	ADP
ap-7354	454	5	the	the	DET
ap-7354	454	6	dirac	dirac	NOUN
ap-7354	454	7	oscillator	oscillator	PROPN
ap-7354	454	8	.	.	PUNCT
ap-7354	455	1	journal	journal	PROPN
ap-7354	455	2	of	of	ADP
ap-7354	455	3	physics	physics	PROPN
ap-7354	455	4	a	a	PRON
ap-7354	455	5	:	:	PUNCT
ap-7354	455	6	mathematical	mathematical	ADJ
ap-7354	455	7	and	and	CCONJ
ap-7354	455	8	general	general	ADJ
ap-7354	455	9	23(12):2263	23(12):2263	NUM
ap-7354	455	10	,	,	PUNCT
ap-7354	455	11	1990	1990	NUM
ap-7354	455	12	.	.	PUNCT
ap-7354	456	1	https://doi.org/10.1088/0305-4470/23/12/011	https://doi.org/10.1088/0305-4470/23/12/011	NOUN
ap-7354	456	2	.	.	PUNCT
ap-7354	457	1	[	[	X
ap-7354	457	2	23	23	NUM
ap-7354	457	3	]	]	X
ap-7354	457	4	o.	o.	PROPN
ap-7354	457	5	l.	l.	PROPN
ap-7354	457	6	de	de	PROPN
ap-7354	457	7	lange	lange	PROPN
ap-7354	457	8	.	.	PUNCT
ap-7354	458	1	shift	shift	NOUN
ap-7354	458	2	operators	operator	NOUN
ap-7354	458	3	for	for	ADP
ap-7354	458	4	a	a	DET
ap-7354	458	5	dirac	dirac	NOUN
ap-7354	458	6	oscillator	oscillator	NOUN
ap-7354	458	7	.	.	PUNCT
ap-7354	459	1	journal	journal	PROPN
ap-7354	459	2	of	of	ADP
ap-7354	459	3	mathematical	mathematical	ADJ
ap-7354	459	4	physics	physics	NOUN
ap-7354	459	5	32(5):1296	32(5):1296	NUM
ap-7354	459	6	,	,	PUNCT
ap-7354	459	7	1991	1991	NUM
ap-7354	459	8	.	.	PUNCT
ap-7354	460	1	https://doi.org/10.1063/1.529328	https://doi.org/10.1063/1.529328	NOUN
ap-7354	460	2	.	.	PUNCT
ap-7354	461	1	701	701	NUM
ap-7354	461	2	https://doi.org/10.1088/1126-6708/1999/09/032	https://doi.org/10.1088/1126-6708/1999/09/032	PROPN
ap-7354	461	3	https://doi.org/10.1007/jhep05(2010)022	https://doi.org/10.1007/jhep05(2010)022	PROPN
ap-7354	461	4	https://doi.org/10.1142/s0217751x09043353	https://doi.org/10.1142/s0217751x09043353	X
ap-7354	461	5	https://doi.org/10.1007/978-3-642-11897-5_1	https://doi.org/10.1007/978-3-642-11897-5_1	X
ap-7354	461	6	https://doi.org/10.1103/physrevlett.86.2716	https://doi.org/10.1103/physrevlett.86.2716	VERB
ap-7354	461	7	https://doi.org/10.14311/ap.2020.60.0111	https://doi.org/10.14311/ap.2020.60.0111	NOUN
ap-7354	461	8	https://doi.org/10.30970/jps.24.2002	https://doi.org/10.30970/jps.24.2002	NOUN
ap-7354	461	9	https://doi.org/10.1103/revmodphys.73.977	https://doi.org/10.1103/revmodphys.73.977	VERB
ap-7354	461	10	https://doi.org/10.30970/jps.24.1801	https://doi.org/10.30970/jps.24.1801	ADJ
ap-7354	461	11	https://doi.org/10.1103/physrev.71.38	https://doi.org/10.1103/physrev.71.38	NOUN
ap-7354	461	12	https://doi.org/10.1103/physrev.72.68	https://doi.org/10.1103/physrev.72.68	PROPN
ap-7354	461	13	https://doi.org/10.1088/1126-6708/2000/05/015	https://doi.org/10.1088/1126-6708/2000/05/015	PROPN
ap-7354	461	14	https://doi.org/10.1016/0370-2693(91)90358-w	https://doi.org/10.1016/0370-2693(91)90358-w	PROPN
ap-7354	461	15	https://doi.org/10.1007/s12043-017-1381-4	https://doi.org/10.1007/s12043-017-1381-4	PRON
ap-7354	461	16	https://doi.org/10.1088/1751-8113/43/34/345401	https://doi.org/10.1088/1751-8113/43/34/345401	NOUN
ap-7354	461	17	https://doi.org/10.1103/physrevd.79.125011	https://doi.org/10.1103/physrevd.79.125011	PROPN
ap-7354	461	18	https://doi.org/10.1007/bf02721775	https://doi.org/10.1007/bf02721775	PROPN
ap-7354	461	19	https://doi.org/10.1088/0305-4470/22/17/002	https://doi.org/10.1088/0305-4470/22/17/002	NOUN
ap-7354	461	20	https://doi.org/10.1063/1.529660	https://doi.org/10.1063/1.529660	PRON
ap-7354	461	21	https://doi.org/10.1103/physrevlett.64.1643	https://doi.org/10.1103/physrevlett.64.1643	VERB
ap-7354	461	22	https://doi.org/10.1088/0305-4470/23/12/011	https://doi.org/10.1088/0305-4470/23/12/011	PROPN
ap-7354	461	23	https://doi.org/10.1063/1.529328	https://doi.org/10.1063/1.529328	PROPN
ap-7354	461	24	ilyas	ilyas	PROPN
ap-7354	461	25	haouam	haouam	VERB
ap-7354	461	26	acta	acta	PROPN
ap-7354	461	27	polytechnica	polytechnica	PROPN
ap-7354	462	1	[	[	X
ap-7354	462	2	24	24	NUM
ap-7354	462	3	]	]	PUNCT
ap-7354	462	4	a.	a.	NOUN
ap-7354	462	5	bermudez	bermudez	PROPN
ap-7354	462	6	,	,	PUNCT
ap-7354	462	7	m.	m.	PROPN
ap-7354	462	8	martin	martin	PROPN
ap-7354	462	9	-	-	PUNCT
ap-7354	462	10	delgado	delgado	PROPN
ap-7354	462	11	,	,	PUNCT
ap-7354	462	12	e.	e.	PROPN
ap-7354	462	13	solano	solano	PROPN
ap-7354	462	14	.	.	PUNCT
ap-7354	463	1	exact	exact	ADJ
ap-7354	463	2	mapping	mapping	NOUN
ap-7354	463	3	of	of	ADP
ap-7354	463	4	the	the	DET
ap-7354	463	5	2	2	NUM
ap-7354	463	6	+	+	SYM
ap-7354	463	7	1	1	NUM
ap-7354	463	8	dirac	dirac	NOUN
ap-7354	463	9	oscillator	oscillator	NOUN
ap-7354	463	10	onto	onto	ADP
ap-7354	463	11	the	the	DET
ap-7354	463	12	jaynes	jayne	NOUN
ap-7354	463	13	-	-	PUNCT
ap-7354	463	14	cummings	cummings	PROPN
ap-7354	463	15	model	model	NOUN
ap-7354	463	16	:	:	PUNCT
ap-7354	463	17	ion	ion	NOUN
ap-7354	463	18	-	-	PUNCT
ap-7354	463	19	trap	trap	NOUN
ap-7354	463	20	experimental	experimental	ADJ
ap-7354	463	21	proposal	proposal	NOUN
ap-7354	463	22	.	.	PUNCT
ap-7354	464	1	physical	physical	ADJ
ap-7354	464	2	review	review	NOUN
ap-7354	464	3	a	a	DET
ap-7354	464	4	76:041801(r	76:041801(r	NOUN
ap-7354	464	5	)	)	PUNCT
ap-7354	464	6	,	,	PUNCT
ap-7354	464	7	2007	2007	NUM
ap-7354	464	8	.	.	PUNCT
ap-7354	465	1	https://doi.org/10.1103/physreva.76.041801	https://doi.org/10.1103/physreva.76.041801	NOUN
ap-7354	465	2	.	.	PUNCT
ap-7354	466	1	[	[	X
ap-7354	466	2	25	25	NUM
ap-7354	466	3	]	]	PUNCT
ap-7354	466	4	a.	a.	NOUN
ap-7354	466	5	bermudez	bermudez	PROPN
ap-7354	466	6	,	,	PUNCT
ap-7354	466	7	m.	m.	NOUN
ap-7354	466	8	a.	a.	PROPN
ap-7354	466	9	martin	martin	PROPN
ap-7354	466	10	-	-	PUNCT
ap-7354	466	11	delgado	delgado	PROPN
ap-7354	466	12	,	,	PUNCT
ap-7354	466	13	a.	a.	PROPN
ap-7354	466	14	luis	luis	PROPN
ap-7354	466	15	.	.	PUNCT
ap-7354	467	1	chirality	chirality	ADJ
ap-7354	467	2	quantum	quantum	NOUN
ap-7354	467	3	phase	phase	NOUN
ap-7354	467	4	transition	transition	NOUN
ap-7354	467	5	in	in	ADP
ap-7354	467	6	the	the	DET
ap-7354	467	7	dirac	dirac	NOUN
ap-7354	467	8	oscillator	oscillator	NOUN
ap-7354	467	9	.	.	PUNCT
ap-7354	468	1	physical	physical	ADJ
ap-7354	468	2	review	review	NOUN
ap-7354	468	3	a	a	DET
ap-7354	468	4	77(6):063815	77(6):063815	NOUN
ap-7354	468	5	,	,	PUNCT
ap-7354	468	6	2008	2008	NUM
ap-7354	468	7	.	.	PUNCT
ap-7354	469	1	https://doi.org/10.1103/physreva.77.063815	https://doi.org/10.1103/physreva.77.063815	PROPN
ap-7354	469	2	.	.	PUNCT
ap-7354	470	1	[	[	X
ap-7354	470	2	26	26	NUM
ap-7354	470	3	]	]	PUNCT
ap-7354	470	4	j.	j.	PROPN
ap-7354	470	5	a.	a.	PROPN
ap-7354	470	6	franco	franco	PROPN
ap-7354	470	7	-	-	PUNCT
ap-7354	470	8	villafañe	villafañe	PROPN
ap-7354	470	9	,	,	PUNCT
ap-7354	470	10	e.	e.	PROPN
ap-7354	470	11	sadurní	sadurní	PROPN
ap-7354	470	12	,	,	PUNCT
ap-7354	470	13	s.	s.	PROPN
ap-7354	470	14	barkhofen	barkhofen	PROPN
ap-7354	470	15	,	,	PUNCT
ap-7354	470	16	et	et	PROPN
ap-7354	470	17	al	al	PROPN
ap-7354	470	18	.	.	PUNCT
ap-7354	471	1	first	first	PROPN
ap-7354	471	2	experimental	experimental	ADJ
ap-7354	471	3	realization	realization	NOUN
ap-7354	471	4	of	of	ADP
ap-7354	471	5	the	the	DET
ap-7354	471	6	dirac	dirac	NOUN
ap-7354	471	7	oscillator	oscillator	NOUN
ap-7354	471	8	.	.	PUNCT
ap-7354	472	1	physical	physical	PROPN
ap-7354	472	2	review	review	PROPN
ap-7354	472	3	letters	letter	NOUN
ap-7354	472	4	111:170405	111:170405	NUM
ap-7354	472	5	,	,	PUNCT
ap-7354	472	6	2013	2013	NUM
ap-7354	472	7	.	.	PUNCT
ap-7354	473	1	https://doi.org/10.1103/physrevlett.111.170405	https://doi.org/10.1103/physrevlett.111.170405	PROPN
ap-7354	473	2	.	.	PUNCT
ap-7354	474	1	[	[	X
ap-7354	474	2	27	27	NUM
ap-7354	474	3	]	]	X
ap-7354	474	4	c.	c.	PROPN
ap-7354	474	5	quimbay	quimbay	PROPN
ap-7354	474	6	,	,	PUNCT
ap-7354	474	7	p.	p.	NOUN
ap-7354	474	8	strange	strange	ADJ
ap-7354	474	9	.	.	PUNCT
ap-7354	475	1	arxiv:1311.2021	arxiv:1311.2021	NOUN
ap-7354	475	2	.	.	PUNCT
ap-7354	476	1	[	[	X
ap-7354	476	2	28	28	NUM
ap-7354	476	3	]	]	X
ap-7354	476	4	c.	c.	PROPN
ap-7354	476	5	quimbay	quimbay	PROPN
ap-7354	476	6	,	,	PUNCT
ap-7354	476	7	p.	p.	NOUN
ap-7354	476	8	strange	strange	ADJ
ap-7354	476	9	.	.	PUNCT
ap-7354	477	1	arxiv:1312.5251	arxiv:1312.5251	NOUN
ap-7354	477	2	.	.	PUNCT
ap-7354	478	1	[	[	X
ap-7354	478	2	29	29	NUM
ap-7354	478	3	]	]	PUNCT
ap-7354	478	4	a.	a.	NOUN
ap-7354	478	5	boumali	boumali	PROPN
ap-7354	478	6	.	.	PUNCT
ap-7354	479	1	thermodynamic	thermodynamic	ADJ
ap-7354	479	2	properties	property	NOUN
ap-7354	479	3	of	of	ADP
ap-7354	479	4	the	the	DET
ap-7354	479	5	graphene	graphene	NOUN
ap-7354	479	6	in	in	ADP
ap-7354	479	7	a	a	DET
ap-7354	479	8	magnetic	magnetic	ADJ
ap-7354	479	9	field	field	NOUN
ap-7354	479	10	via	via	ADP
ap-7354	479	11	the	the	DET
ap-7354	479	12	two	two	NUM
ap-7354	479	13	-	-	PUNCT
ap-7354	479	14	dimensional	dimensional	ADJ
ap-7354	479	15	dirac	dirac	NOUN
ap-7354	479	16	oscillator	oscillator	NOUN
ap-7354	479	17	.	.	PUNCT
ap-7354	480	1	physica	physica	PROPN
ap-7354	480	2	scripta	scripta	PROPN
ap-7354	480	3	90(4):045702	90(4):045702	PROPN
ap-7354	480	4	,	,	PUNCT
ap-7354	480	5	2015	2015	NUM
ap-7354	480	6	.	.	PUNCT
ap-7354	481	1	https://doi.org/10.1088/0031-8949/90/4/045702	https://doi.org/10.1088/0031-8949/90/4/045702	NOUN
ap-7354	481	2	.	.	PUNCT
ap-7354	482	1	[	[	X
ap-7354	482	2	30	30	NUM
ap-7354	482	3	]	]	X
ap-7354	482	4	b.	b.	PROPN
ap-7354	482	5	bagchi	bagchi	PROPN
ap-7354	482	6	,	,	PUNCT
ap-7354	482	7	a.	a.	NOUN
ap-7354	482	8	fring	fring	NOUN
ap-7354	482	9	.	.	PUNCT
ap-7354	483	1	minimal	minimal	ADJ
ap-7354	483	2	length	length	NOUN
ap-7354	483	3	in	in	ADP
ap-7354	483	4	quantum	quantum	ADJ
ap-7354	483	5	mechanics	mechanic	NOUN
ap-7354	483	6	and	and	CCONJ
ap-7354	483	7	non	non	ADJ
ap-7354	483	8	-	-	ADJ
ap-7354	483	9	hermitian	hermitian	ADJ
ap-7354	483	10	hamiltonian	hamiltonian	ADJ
ap-7354	483	11	systems	system	NOUN
ap-7354	483	12	.	.	PUNCT
ap-7354	484	1	physics	physics	NOUN
ap-7354	484	2	letters	letter	NOUN
ap-7354	484	3	a	a	DET
ap-7354	484	4	373(47):4307–4310	373(47):4307–4310	NUM
ap-7354	484	5	,	,	PUNCT
ap-7354	484	6	2009	2009	NUM
ap-7354	484	7	.	.	PUNCT
ap-7354	485	1	https://doi.org/10.1016/j.physleta.2009.09.054	https://doi.org/10.1016/j.physleta.2009.09.054	ADJ
ap-7354	485	2	.	.	PUNCT
ap-7354	486	1	[	[	X
ap-7354	486	2	31	31	NUM
ap-7354	486	3	]	]	PUNCT
ap-7354	486	4	i.	i.	PROPN
ap-7354	486	5	haouam	haouam	PROPN
ap-7354	486	6	.	.	PUNCT
ap-7354	487	1	the	the	DET
ap-7354	487	2	non	non	ADJ
ap-7354	487	3	-	-	ADJ
ap-7354	487	4	relativistic	relativistic	ADJ
ap-7354	487	5	limit	limit	NOUN
ap-7354	487	6	of	of	ADP
ap-7354	487	7	the	the	DET
ap-7354	487	8	dkp	dkp	PROPN
ap-7354	487	9	equation	equation	NOUN
ap-7354	487	10	in	in	ADP
ap-7354	487	11	non	non	ADJ
ap-7354	487	12	-	-	ADJ
ap-7354	487	13	commutative	commutative	ADJ
ap-7354	487	14	phase	phase	NOUN
ap-7354	487	15	-	-	PUNCT
ap-7354	487	16	space	space	NOUN
ap-7354	487	17	.	.	PUNCT
ap-7354	488	1	symmetry	symmetry	NOUN
ap-7354	488	2	11(2):223	11(2):223	NUM
ap-7354	488	3	,	,	PUNCT
ap-7354	488	4	2019	2019	NUM
ap-7354	488	5	.	.	PUNCT
ap-7354	489	1	https://doi.org/10.3390/sym11020223	https://doi.org/10.3390/sym11020223	PROPN
ap-7354	489	2	.	.	PUNCT
ap-7354	490	1	[	[	X
ap-7354	490	2	32	32	NUM
ap-7354	490	3	]	]	PUNCT
ap-7354	490	4	b.	b.	PROPN
ap-7354	490	5	mandal	mandal	PROPN
ap-7354	490	6	,	,	PUNCT
ap-7354	490	7	s.	s.	PROPN
ap-7354	490	8	verma	verma	PROPN
ap-7354	490	9	.	.	PUNCT
ap-7354	490	10	dirac	dirac	NOUN
ap-7354	490	11	oscillator	oscillator	NOUN
ap-7354	490	12	in	in	ADP
ap-7354	490	13	an	an	DET
ap-7354	490	14	external	external	ADJ
ap-7354	490	15	magnetic	magnetic	ADJ
ap-7354	490	16	field	field	NOUN
ap-7354	490	17	.	.	PUNCT
ap-7354	491	1	physics	physics	NOUN
ap-7354	491	2	letters	letter	NOUN
ap-7354	491	3	a	a	DET
ap-7354	491	4	374(8):1021–1023	374(8):1021–1023	NUM
ap-7354	491	5	,	,	PUNCT
ap-7354	491	6	2010	2010	NUM
ap-7354	491	7	.	.	PUNCT
ap-7354	492	1	https://doi.org/10.1016/j.physleta.2009.12.048	https://doi.org/10.1016/j.physleta.2009.12.048	NOUN
ap-7354	492	2	.	.	PUNCT
ap-7354	493	1	[	[	X
ap-7354	493	2	33	33	NUM
ap-7354	493	3	]	]	PUNCT
ap-7354	493	4	a.	a.	NOUN
ap-7354	493	5	boumali	boumali	PROPN
ap-7354	493	6	,	,	PUNCT
ap-7354	493	7	h.	h.	PROPN
ap-7354	493	8	hassanabadi	hassanabadi	PROPN
ap-7354	493	9	.	.	PUNCT
ap-7354	494	1	the	the	DET
ap-7354	494	2	thermal	thermal	ADJ
ap-7354	494	3	properties	property	NOUN
ap-7354	494	4	of	of	ADP
ap-7354	494	5	a	a	DET
ap-7354	494	6	two	two	NUM
ap-7354	494	7	-	-	PUNCT
ap-7354	494	8	dimensional	dimensional	ADJ
ap-7354	494	9	dirac	dirac	NOUN
ap-7354	494	10	oscillator	oscillator	NOUN
ap-7354	494	11	under	under	ADP
ap-7354	494	12	an	an	DET
ap-7354	494	13	external	external	ADJ
ap-7354	494	14	magnetic	magnetic	ADJ
ap-7354	494	15	field	field	NOUN
ap-7354	494	16	.	.	PUNCT
ap-7354	495	1	the	the	DET
ap-7354	495	2	european	european	PROPN
ap-7354	495	3	physical	physical	PROPN
ap-7354	495	4	journal	journal	PROPN
ap-7354	495	5	plus	plus	CCONJ
ap-7354	495	6	128:124	128:124	NUM
ap-7354	495	7	,	,	PUNCT
ap-7354	495	8	2013	2013	NUM
ap-7354	495	9	.	.	PUNCT
ap-7354	496	1	https://doi.org/10.1140/epjp/i2013-13124-y	https://doi.org/10.1140/epjp/i2013-13124-y	PROPN
ap-7354	496	2	.	.	PUNCT
ap-7354	497	1	[	[	X
ap-7354	497	2	34	34	NUM
ap-7354	497	3	]	]	PUNCT
ap-7354	497	4	a.	a.	NOUN
ap-7354	497	5	bermudez	bermudez	PROPN
ap-7354	497	6	,	,	PUNCT
ap-7354	497	7	m.	m.	NOUN
ap-7354	497	8	a.	a.	PROPN
ap-7354	497	9	martin	martin	PROPN
ap-7354	497	10	-	-	PUNCT
ap-7354	497	11	delgado	delgado	PROPN
ap-7354	497	12	,	,	PUNCT
ap-7354	497	13	e.	e.	PROPN
ap-7354	497	14	solano	solano	PROPN
ap-7354	497	15	.	.	PROPN
ap-7354	497	16	mesoscopic	mesoscopic	PROPN
ap-7354	497	17	superposition	superposition	NOUN
ap-7354	497	18	states	state	NOUN
ap-7354	497	19	in	in	ADP
ap-7354	497	20	relativistic	relativistic	ADJ
ap-7354	497	21	landau	landau	NOUN
ap-7354	497	22	levels	level	NOUN
ap-7354	497	23	.	.	PUNCT
ap-7354	498	1	physical	physical	ADJ
ap-7354	498	2	review	review	NOUN
ap-7354	498	3	letters	letter	NOUN
ap-7354	498	4	99:123602	99:123602	PRON
ap-7354	498	5	,	,	PUNCT
ap-7354	498	6	2007	2007	NUM
ap-7354	498	7	.	.	PUNCT
ap-7354	499	1	https://doi.org/10.1103/physrevlett.99.123602	https://doi.org/10.1103/physrevlett.99.123602	INTJ
ap-7354	499	2	.	.	PUNCT
ap-7354	500	1	[	[	X
ap-7354	500	2	35	35	NUM
ap-7354	500	3	]	]	PUNCT
ap-7354	500	4	j.	j.	PROPN
ap-7354	500	5	j.	j.	PROPN
ap-7354	500	6	sakurai	sakurai	PROPN
ap-7354	500	7	.	.	PUNCT
ap-7354	501	1	modern	modern	ADJ
ap-7354	501	2	quantum	quantum	ADJ
ap-7354	501	3	mechanics	mechanic	NOUN
ap-7354	501	4	.	.	PUNCT
ap-7354	502	1	(	(	PUNCT
ap-7354	502	2	revised	revise	VERB
ap-7354	502	3	edition	edition	NOUN
ap-7354	502	4	)	)	PUNCT
ap-7354	502	5	.	.	PUNCT
ap-7354	503	1	addison	addison	PROPN
ap-7354	503	2	-	-	PUNCT
ap-7354	503	3	wesley	wesley	PROPN
ap-7354	503	4	,	,	PUNCT
ap-7354	503	5	1994	1994	NUM
ap-7354	503	6	.	.	PUNCT
ap-7354	504	1	[	[	X
ap-7354	504	2	36	36	NUM
ap-7354	504	3	]	]	X
ap-7354	504	4	s.	s.	PROPN
ap-7354	504	5	cai	cai	PROPN
ap-7354	504	6	,	,	PUNCT
ap-7354	504	7	t.	t.	PROPN
ap-7354	504	8	jing	jing	PROPN
ap-7354	504	9	,	,	PUNCT
ap-7354	504	10	g.	g.	PROPN
ap-7354	504	11	guo	guo	PROPN
ap-7354	504	12	,	,	PUNCT
ap-7354	504	13	et	et	PROPN
ap-7354	504	14	al	al	PROPN
ap-7354	504	15	.	.	PROPN
ap-7354	504	16	dirac	dirac	PROPN
ap-7354	504	17	oscillator	oscillator	PROPN
ap-7354	504	18	in	in	ADP
ap-7354	504	19	noncommutative	noncommutative	ADJ
ap-7354	504	20	phase	phase	NOUN
ap-7354	504	21	space	space	NOUN
ap-7354	504	22	.	.	PUNCT
ap-7354	505	1	international	international	ADJ
ap-7354	505	2	journal	journal	PROPN
ap-7354	505	3	of	of	ADP
ap-7354	505	4	theoretical	theoretical	ADJ
ap-7354	505	5	physics	physics	NOUN
ap-7354	505	6	49:1699–1705	49:1699–1705	NUM
ap-7354	505	7	,	,	PUNCT
ap-7354	505	8	2010	2010	NUM
ap-7354	505	9	.	.	PUNCT
ap-7354	505	10	https://doi.org/10.1007/s10773-010-0349-7	https://doi.org/10.1007/s10773-010-0349-7	NUM
ap-7354	505	11	.	.	PUNCT
ap-7354	506	1	[	[	X
ap-7354	506	2	37	37	NUM
ap-7354	506	3	]	]	PUNCT
ap-7354	506	4	b.	b.	PROPN
ap-7354	506	5	p.	p.	PROPN
ap-7354	506	6	mandal	mandal	PROPN
ap-7354	506	7	,	,	PUNCT
ap-7354	506	8	s.	s.	PROPN
ap-7354	506	9	k.	k.	PROPN
ap-7354	506	10	rai	rai	PROPN
ap-7354	506	11	.	.	PROPN
ap-7354	506	12	noncommutative	noncommutative	PROPN
ap-7354	506	13	dirac	dirac	PROPN
ap-7354	506	14	oscillator	oscillator	NOUN
ap-7354	506	15	in	in	ADP
ap-7354	506	16	an	an	DET
ap-7354	506	17	external	external	ADJ
ap-7354	506	18	magnetic	magnetic	ADJ
ap-7354	506	19	field	field	NOUN
ap-7354	506	20	.	.	PUNCT
ap-7354	507	1	physics	physics	NOUN
ap-7354	507	2	letters	letter	NOUN
ap-7354	507	3	a	a	DET
ap-7354	507	4	376(36):2467–2470	376(36):2467–2470	NUM
ap-7354	507	5	,	,	PUNCT
ap-7354	507	6	2012	2012	NUM
ap-7354	507	7	.	.	PUNCT
ap-7354	508	1	https://doi.org/10.1016/j.physleta.2012.07.001	https://doi.org/10.1016/j.physleta.2012.07.001	NOUN
ap-7354	508	2	.	.	PUNCT
ap-7354	509	1	[	[	X
ap-7354	509	2	38	38	NUM
ap-7354	509	3	]	]	PUNCT
ap-7354	509	4	m.	m.	NOUN
ap-7354	509	5	hosseinpour	hosseinpour	PROPN
ap-7354	509	6	,	,	PUNCT
ap-7354	509	7	h.	h.	PROPN
ap-7354	509	8	hassanabadi	hassanabadi	PROPN
ap-7354	509	9	,	,	PUNCT
ap-7354	509	10	m.	m.	NOUN
ap-7354	509	11	de	de	PROPN
ap-7354	509	12	montigny	montigny	PROPN
ap-7354	509	13	.	.	PUNCT
ap-7354	510	1	the	the	DET
ap-7354	510	2	dirac	dirac	NOUN
ap-7354	510	3	oscillator	oscillator	NOUN
ap-7354	510	4	in	in	ADP
ap-7354	510	5	a	a	DET
ap-7354	510	6	spinning	spin	VERB
ap-7354	510	7	cosmic	cosmic	ADJ
ap-7354	510	8	string	string	NOUN
ap-7354	510	9	spacetime	spacetime	NOUN
ap-7354	510	10	.	.	PUNCT
ap-7354	511	1	the	the	DET
ap-7354	511	2	european	european	PROPN
ap-7354	511	3	physical	physical	PROPN
ap-7354	511	4	journal	journal	PROPN
ap-7354	511	5	c	c	PROPN
ap-7354	511	6	79:311	79:311	NUM
ap-7354	511	7	,	,	PUNCT
ap-7354	511	8	2019	2019	NUM
ap-7354	511	9	.	.	PUNCT
ap-7354	512	1	https://doi.org/10.1140/epjc/s10052-019-6830-4	https://doi.org/10.1140/epjc/s10052-019-6830-4	PROPN
ap-7354	512	2	.	.	PUNCT
ap-7354	513	1	[	[	X
ap-7354	513	2	39	39	NUM
ap-7354	513	3	]	]	PUNCT
ap-7354	513	4	m.	m.	NOUN
ap-7354	513	5	de	de	PROPN
ap-7354	513	6	montigny	montigny	PROPN
ap-7354	513	7	,	,	PUNCT
ap-7354	513	8	s.	s.	PROPN
ap-7354	513	9	zare	zare	PROPN
ap-7354	513	10	,	,	PUNCT
ap-7354	513	11	h.	h.	PROPN
ap-7354	513	12	hassanabadi	hassanabadi	PROPN
ap-7354	513	13	.	.	PUNCT
ap-7354	514	1	fermi	fermi	NOUN
ap-7354	514	2	field	field	NOUN
ap-7354	514	3	and	and	CCONJ
ap-7354	514	4	dirac	dirac	NOUN
ap-7354	514	5	oscillator	oscillator	NOUN
ap-7354	514	6	in	in	ADP
ap-7354	514	7	a	a	DET
ap-7354	514	8	som	som	NOUN
ap-7354	514	9	-	-	PUNCT
ap-7354	514	10	raychaudhuri	raychaudhuri	NOUN
ap-7354	514	11	space	space	NOUN
ap-7354	514	12	-	-	PUNCT
ap-7354	514	13	time	time	NOUN
ap-7354	514	14	.	.	PUNCT
ap-7354	515	1	general	general	ADJ
ap-7354	515	2	relativity	relativity	NOUN
ap-7354	515	3	and	and	CCONJ
ap-7354	515	4	gravitation	gravitation	NOUN
ap-7354	515	5	volume	volume	NOUN
ap-7354	515	6	50:47	50:47	NUM
ap-7354	515	7	,	,	PUNCT
ap-7354	515	8	2018	2018	NUM
ap-7354	515	9	.	.	PUNCT
ap-7354	516	1	https://doi.org/10.1007/s10714-018-2370-8	https://doi.org/10.1007/s10714-018-2370-8	X
ap-7354	516	2	.	.	PUNCT
ap-7354	517	1	[	[	X
ap-7354	517	2	40	40	NUM
ap-7354	517	3	]	]	PUNCT
ap-7354	517	4	k.	k.	PROPN
ap-7354	517	5	bakke	bakke	PROPN
ap-7354	517	6	,	,	PUNCT
ap-7354	517	7	h.	h.	PROPN
ap-7354	517	8	mota	mota	PROPN
ap-7354	517	9	.	.	PUNCT
ap-7354	518	1	dirac	dirac	NOUN
ap-7354	518	2	oscillator	oscillator	NOUN
ap-7354	518	3	in	in	ADP
ap-7354	518	4	the	the	DET
ap-7354	518	5	cosmic	cosmic	ADJ
ap-7354	518	6	string	string	NOUN
ap-7354	518	7	spacetime	spacetime	NOUN
ap-7354	518	8	in	in	ADP
ap-7354	518	9	the	the	DET
ap-7354	518	10	context	context	NOUN
ap-7354	518	11	of	of	ADP
ap-7354	518	12	gravity	gravity	NOUN
ap-7354	518	13	’s	’s	PART
ap-7354	518	14	rainbow	rainbow	NOUN
ap-7354	518	15	.	.	PUNCT
ap-7354	519	1	the	the	DET
ap-7354	519	2	european	european	PROPN
ap-7354	519	3	physical	physical	PROPN
ap-7354	519	4	journal	journal	PROPN
ap-7354	519	5	plus	plus	CCONJ
ap-7354	519	6	133:409	133:409	NUM
ap-7354	519	7	,	,	PUNCT
ap-7354	519	8	2018	2018	NUM
ap-7354	519	9	.	.	PUNCT
ap-7354	520	1	https://doi.org/10.1140/epjp/i2018-12268-6	https://doi.org/10.1140/epjp/i2018-12268-6	X
ap-7354	520	2	.	.	PUNCT
ap-7354	521	1	[	[	X
ap-7354	521	2	41	41	NUM
ap-7354	521	3	]	]	X
ap-7354	521	4	h.	h.	PROPN
ap-7354	521	5	chen	chen	PROPN
ap-7354	521	6	,	,	PUNCT
ap-7354	521	7	z.-w	z.-w	PROPN
ap-7354	521	8	.	.	PUNCT
ap-7354	522	1	long	long	ADV
ap-7354	522	2	,	,	PUNCT
ap-7354	522	3	y.	y.	PROPN
ap-7354	522	4	yang	yang	PROPN
ap-7354	522	5	,	,	PUNCT
ap-7354	522	6	c.-y	c.-y	NOUN
ap-7354	522	7	.	.	PUNCT
ap-7354	523	1	long	long	ADV
ap-7354	523	2	.	.	PUNCT
ap-7354	524	1	study	study	NOUN
ap-7354	524	2	of	of	ADP
ap-7354	524	3	the	the	DET
ap-7354	524	4	dirac	dirac	NOUN
ap-7354	524	5	oscillator	oscillator	NOUN
ap-7354	524	6	in	in	ADP
ap-7354	524	7	the	the	DET
ap-7354	524	8	presence	presence	NOUN
ap-7354	524	9	of	of	ADP
ap-7354	524	10	vector	vector	NOUN
ap-7354	524	11	and	and	CCONJ
ap-7354	524	12	scalar	scalar	ADJ
ap-7354	524	13	potentials	potential	NOUN
ap-7354	524	14	in	in	ADP
ap-7354	524	15	the	the	DET
ap-7354	524	16	cosmic	cosmic	ADJ
ap-7354	524	17	string	string	NOUN
ap-7354	524	18	space	space	NOUN
ap-7354	524	19	-	-	PUNCT
ap-7354	524	20	time	time	NOUN
ap-7354	524	21	.	.	PUNCT
ap-7354	525	1	modern	modern	ADJ
ap-7354	525	2	physics	physics	NOUN
ap-7354	525	3	letters	letter	NOUN
ap-7354	525	4	a	a	DET
ap-7354	525	5	35(21):2050179	35(21):2050179	NUM
ap-7354	525	6	,	,	PUNCT
ap-7354	525	7	2020	2020	NUM
ap-7354	525	8	.	.	PUNCT
ap-7354	526	1	https://doi.org/10.1142/s0217732320501795	https://doi.org/10.1142/s0217732320501795	NUM
ap-7354	526	2	.	.	PUNCT
ap-7354	527	1	[	[	X
ap-7354	527	2	42	42	NUM
ap-7354	527	3	]	]	X
ap-7354	527	4	f.	f.	PROPN
ap-7354	527	5	ahmed	ahmed	PROPN
ap-7354	527	6	.	.	PUNCT
ap-7354	528	1	interaction	interaction	NOUN
ap-7354	528	2	of	of	ADP
ap-7354	528	3	the	the	DET
ap-7354	528	4	dirac	dirac	NOUN
ap-7354	528	5	oscillator	oscillator	NOUN
ap-7354	528	6	with	with	ADP
ap-7354	528	7	the	the	DET
ap-7354	528	8	aharonov	aharonov	PROPN
ap-7354	528	9	-	-	PUNCT
ap-7354	528	10	bohm	bohm	PROPN
ap-7354	528	11	potential	potential	NOUN
ap-7354	528	12	in	in	ADP
ap-7354	528	13	(	(	PUNCT
ap-7354	528	14	1	1	NUM
ap-7354	528	15	+	+	NOUN
ap-7354	528	16	2)-dimensional	2)-dimensional	PROPN
ap-7354	528	17	gürses	gürse	NOUN
ap-7354	528	18	space	space	NOUN
ap-7354	528	19	-	-	PUNCT
ap-7354	528	20	time	time	NOUN
ap-7354	528	21	backgrounds	background	NOUN
ap-7354	528	22	.	.	PUNCT
ap-7354	529	1	annals	annal	NOUN
ap-7354	529	2	of	of	ADP
ap-7354	529	3	physics	physics	NOUN
ap-7354	529	4	415:168113	415:168113	NUM
ap-7354	529	5	,	,	PUNCT
ap-7354	529	6	2020	2020	NUM
ap-7354	529	7	.	.	PUNCT
ap-7354	530	1	https://doi.org/10.1016/j.aop.2020.168113	https://doi.org/10.1016/j.aop.2020.168113	PROPN
ap-7354	530	2	.	.	PUNCT
ap-7354	531	1	[	[	X
ap-7354	531	2	43	43	NUM
ap-7354	531	3	]	]	X
ap-7354	531	4	d.	d.	PROPN
ap-7354	531	5	f.	f.	PROPN
ap-7354	531	6	lima	lima	PROPN
ap-7354	531	7	,	,	PUNCT
ap-7354	531	8	f.	f.	PROPN
ap-7354	531	9	m.	m.	PROPN
ap-7354	531	10	andrade	andrade	PROPN
ap-7354	531	11	,	,	PUNCT
ap-7354	531	12	l.	l.	PROPN
ap-7354	531	13	b.	b.	PROPN
ap-7354	531	14	castro	castro	PROPN
ap-7354	531	15	,	,	PUNCT
ap-7354	531	16	et	et	PROPN
ap-7354	531	17	al	al	PROPN
ap-7354	531	18	.	.	PROPN
ap-7354	532	1	on	on	ADP
ap-7354	532	2	the	the	DET
ap-7354	532	3	2d	2d	PROPN
ap-7354	532	4	dirac	dirac	NOUN
ap-7354	532	5	oscillator	oscillator	NOUN
ap-7354	532	6	in	in	ADP
ap-7354	532	7	the	the	DET
ap-7354	532	8	presence	presence	NOUN
ap-7354	532	9	of	of	ADP
ap-7354	532	10	vector	vector	NOUN
ap-7354	532	11	and	and	CCONJ
ap-7354	532	12	scalar	scalar	ADJ
ap-7354	532	13	potentials	potential	NOUN
ap-7354	532	14	in	in	ADP
ap-7354	532	15	the	the	DET
ap-7354	532	16	cosmic	cosmic	ADJ
ap-7354	532	17	string	string	NOUN
ap-7354	532	18	spacetime	spacetime	NOUN
ap-7354	532	19	in	in	ADP
ap-7354	532	20	the	the	DET
ap-7354	532	21	context	context	NOUN
ap-7354	532	22	of	of	ADP
ap-7354	532	23	spin	spin	NOUN
ap-7354	532	24	and	and	CCONJ
ap-7354	532	25	pseudospin	pseudospin	ADJ
ap-7354	532	26	symmetries	symmetry	NOUN
ap-7354	532	27	.	.	PUNCT
ap-7354	533	1	the	the	DET
ap-7354	533	2	european	european	PROPN
ap-7354	533	3	physical	physical	PROPN
ap-7354	533	4	journal	journal	PROPN
ap-7354	533	5	c	c	PROPN
ap-7354	533	6	79:596	79:596	NUM
ap-7354	533	7	,	,	PUNCT
ap-7354	533	8	2019	2019	NUM
ap-7354	533	9	.	.	PUNCT
ap-7354	534	1	https://doi.org/10.1140/epjc/s10052-019-7115-7	https://doi.org/10.1140/epjc/s10052-019-7115-7	VERB
ap-7354	534	2	.	.	PUNCT
ap-7354	535	1	[	[	X
ap-7354	535	2	44	44	NUM
ap-7354	535	3	]	]	PUNCT
ap-7354	535	4	o.	o.	PROPN
ap-7354	535	5	bertolami	bertolami	PROPN
ap-7354	535	6	,	,	PUNCT
ap-7354	535	7	j.	j.	PROPN
ap-7354	535	8	g.	g.	PROPN
ap-7354	535	9	rosa	rosa	PROPN
ap-7354	535	10	,	,	PUNCT
ap-7354	535	11	c.	c.	PROPN
ap-7354	535	12	m.	m.	PROPN
ap-7354	535	13	l.	l.	PROPN
ap-7354	535	14	de	de	PROPN
ap-7354	535	15	aragão	aragão	PROPN
ap-7354	535	16	,	,	PUNCT
ap-7354	535	17	et	et	PROPN
ap-7354	536	1	al	al	PROPN
ap-7354	536	2	.	.	PUNCT
ap-7354	536	3	noncommutative	noncommutative	PROPN
ap-7354	536	4	gravitational	gravitational	ADJ
ap-7354	536	5	quantum	quantum	NOUN
ap-7354	536	6	well	well	NOUN
ap-7354	536	7	.	.	PUNCT
ap-7354	537	1	physical	physical	ADJ
ap-7354	537	2	review	review	PROPN
ap-7354	538	1	d	d	PROPN
ap-7354	538	2	72:025010	72:025010	NUM
ap-7354	538	3	,	,	PUNCT
ap-7354	538	4	2005	2005	NUM
ap-7354	538	5	.	.	PUNCT
ap-7354	539	1	https://doi.org/10.1103/physrevd.72.025010	https://doi.org/10.1103/physrevd.72.025010	NOUN
ap-7354	539	2	.	.	PUNCT
ap-7354	540	1	[	[	X
ap-7354	540	2	45	45	NUM
ap-7354	540	3	]	]	PUNCT
ap-7354	540	4	s.	s.	PROPN
ap-7354	540	5	a.	a.	PROPN
ap-7354	540	6	alavi	alavi	PROPN
ap-7354	540	7	,	,	PUNCT
ap-7354	540	8	m.	m.	NOUN
ap-7354	540	9	a.	a.	NOUN
ap-7354	540	10	nasab	nasab	PROPN
ap-7354	540	11	.	.	PUNCT
ap-7354	541	1	gravitational	gravitational	ADJ
ap-7354	541	2	radiation	radiation	NOUN
ap-7354	541	3	in	in	ADP
ap-7354	541	4	dynamical	dynamical	ADJ
ap-7354	541	5	noncommutative	noncommutative	ADJ
ap-7354	541	6	spaces	space	NOUN
ap-7354	541	7	.	.	PUNCT
ap-7354	542	1	general	general	ADJ
ap-7354	542	2	relativity	relativity	NOUN
ap-7354	542	3	and	and	CCONJ
ap-7354	542	4	gravitation	gravitation	NOUN
ap-7354	542	5	49:5	49:5	NOUN
ap-7354	542	6	,	,	PUNCT
ap-7354	542	7	2017	2017	NUM
ap-7354	542	8	.	.	PUNCT
ap-7354	543	1	https://doi.org/10.1007/s10714-016-2167-6	https://doi.org/10.1007/s10714-016-2167-6	NUM
ap-7354	543	2	.	.	PUNCT
ap-7354	544	1	702	702	NUM
ap-7354	544	2	https://doi.org/10.1103/physreva.76.041801	https://doi.org/10.1103/physreva.76.041801	NOUN
ap-7354	544	3	https://doi.org/10.1103/physreva.77.063815	https://doi.org/10.1103/physreva.77.063815	AUX
ap-7354	544	4	https://doi.org/10.1103/physrevlett.111.170405	https://doi.org/10.1103/physrevlett.111.170405	PROPN
ap-7354	544	5	http://arxiv.org/abs/1311.2021	http://arxiv.org/abs/1311.2021	NOUN
ap-7354	544	6	http://arxiv.org/abs/1312.5251	http://arxiv.org/abs/1312.5251	PROPN
ap-7354	544	7	https://doi.org/10.1088/0031-8949/90/4/045702	https://doi.org/10.1088/0031-8949/90/4/045702	PROPN
ap-7354	544	8	https://doi.org/10.1016/j.physleta.2009.09.054	https://doi.org/10.1016/j.physleta.2009.09.054	PROPN
ap-7354	544	9	https://doi.org/10.3390/sym11020223	https://doi.org/10.3390/sym11020223	NOUN
ap-7354	544	10	https://doi.org/10.1016/j.physleta.2009.12.048	https://doi.org/10.1016/j.physleta.2009.12.048	ADJ
ap-7354	544	11	https://doi.org/10.1140/epjp/i2013-13124-y	https://doi.org/10.1140/epjp/i2013-13124-y	PUNCT
ap-7354	544	12	https://doi.org/10.1103/physrevlett.99.123602	https://doi.org/10.1103/physrevlett.99.123602	PROPN
ap-7354	544	13	https://doi.org/10.1007/s10773-010-0349-7	https://doi.org/10.1007/s10773-010-0349-7	NUM
ap-7354	544	14	https://doi.org/10.1016/j.physleta.2012.07.001	https://doi.org/10.1016/j.physleta.2012.07.001	NOUN
ap-7354	544	15	https://doi.org/10.1140/epjc/s10052-019-6830-4	https://doi.org/10.1140/epjc/s10052-019-6830-4	PROPN
ap-7354	544	16	https://doi.org/10.1007/s10714-018-2370-8	https://doi.org/10.1007/s10714-018-2370-8	PROPN
ap-7354	544	17	https://doi.org/10.1140/epjp/i2018-12268-6	https://doi.org/10.1140/epjp/i2018-12268-6	PRON
ap-7354	544	18	https://doi.org/10.1142/s0217732320501795	https://doi.org/10.1142/s0217732320501795	NUM
ap-7354	544	19	https://doi.org/10.1016/j.aop.2020.168113	https://doi.org/10.1016/j.aop.2020.168113	PROPN
ap-7354	544	20	https://doi.org/10.1140/epjc/s10052-019-7115-7	https://doi.org/10.1140/epjc/s10052-019-7115-7	PROPN
ap-7354	544	21	https://doi.org/10.1103/physrevd.72.025010	https://doi.org/10.1103/physrevd.72.025010	NOUN
ap-7354	544	22	https://doi.org/10.1007/s10714-016-2167-6	https://doi.org/10.1007/s10714-016-2167-6	NUM
ap-7354	544	23	acta	acta	PROPN
ap-7354	544	24	polytechnica	polytechnica	PROPN
ap-7354	544	25	61(6):689–702	61(6):689–702	PROPN
ap-7354	544	26	,	,	PUNCT
ap-7354	544	27	2021	2021	NUM
ap-7354	544	28	1	1	NUM
ap-7354	544	29	introduction	introduction	NOUN
ap-7354	544	30	2	2	NUM
ap-7354	544	31	review	review	NOUN
ap-7354	544	32	of	of	ADP
ap-7354	544	33	dynamical	dynamical	ADJ
ap-7354	544	34	noncommutativity	noncommutativity	NOUN
ap-7354	544	35	3	3	NUM
ap-7354	544	36	two	two	NUM
ap-7354	544	37	-	-	PUNCT
ap-7354	544	38	dimensional	dimensional	ADJ
ap-7354	544	39	dirac	dirac	NOUN
ap-7354	544	40	oscillator	oscillator	NOUN
ap-7354	544	41	in	in	ADP
ap-7354	544	42	dynamical	dynamical	ADJ
ap-7354	544	43	noncommutative	noncommutative	ADJ
ap-7354	544	44	space	space	NOUN
ap-7354	544	45	3.1	3.1	NUM
ap-7354	544	46	extension	extension	NOUN
ap-7354	544	47	to	to	ADP
ap-7354	544	48	dynamical	dynamical	ADJ
ap-7354	544	49	noncommutative	noncommutative	ADJ
ap-7354	544	50	space	space	NOUN
ap-7354	544	51	3.2	3.2	NUM
ap-7354	544	52	unperturbed	unperturbed	ADJ
ap-7354	544	53	eigenvalues	eigenvalue	NOUN
ap-7354	544	54	and	and	CCONJ
ap-7354	544	55	eigenvectors	eigenvector	NOUN
ap-7354	544	56	3.3	3.3	NUM
ap-7354	544	57	perturbed	perturb	VERB
ap-7354	544	58	system	system	NOUN
ap-7354	544	59	4	4	NUM
ap-7354	544	60	conclusion	conclusion	NOUN
ap-7354	544	61	references	reference	NOUN